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Metrol. Meas. Syst., Vol. 24 (2017), No. 2, pp. 229–240.

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Article history: received on Mar. 01, 2017; accepted on Apr. 26, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0036.


Index 330930, ISSN 0860-8229

www.metrology.pg.gda.pl

EFFECT OF FEATURE EXTRACTION ON AUTOMATIC SLEEP STAGE

CLASSIFICATION BY ARTIFICIAL NEURAL NETWORK

Monika Prucnal, Adam G. Polak

Wrocław University of Science and Technology, Faculty of Electronics, B. Prusa 53/55, 50-317 Wrocław, Poland ( [email protected], +48 71 320 6247, [email protected])

Abstract

EEG signal-based sleep stage classification facilitates an initial diagnosis of sleep disorders. The aim of this study

was to compare the efficiency of three methods for feature extraction: power spectral density (PSD), discrete

wavelet transform (DWT) and empirical mode decomposition (EMD) in the automatic classification of sleep stages

by an artificial neural network (ANN). 13650 30-second EEG epochs from the PhysioNet database, representing five sleep stages (W, N1-N3 and REM), were transformed into feature vectors using the aforementioned methods

and principal component analysis (PCA). Three feed-forward ANNs with the same optimal structure (12 input

neurons, 23 + 22 neurons in two hidden layers and 5 output neurons) were trained using three sets of features,

obtained with one of the compared methods each. Calculating PSD from EEG epochs in frequency sub-bands

corresponding to the brain waves (81.1% accuracy for the testing set, comparing with 74.2% for DWT and 57.6%

for EMD) appeared to be the most effective feature extraction method in the analysed problem.

Keywords: sleep stage classification, EEG signal, power spectral density, discrete wavelet transform, empirical

mode decomposition, artificial neural network.

© 2017 Polish Academy of Sciences. All rights reserved

1. Introduction

Sleep is one of the basic modes of human brain activity. It is a recurring state of mind and body characterised by altered consciousness and body stillness. It is well known that adults spend about 1/3 of their life in sleeping, therefore a right quality and amount of sleep have

a significant impact on human mood and health. There is a large group of sleep disorders related to the respiratory, nervous and other

physiological systems, typically monitored by polysomnography [1]. Among them, hyperventilation and sleep apnea are the most prevalent ones. Interrelations between pathology,

system functions and recorded biophysical signals are generally complex [2]. One of approaches to improve at-home patient care is the use of tele-monitoring [3].

Loomis at al. were the first observing that the pattern of brain potentials alters systematically

in a sleeping person [4]. These cyclic shifts of brain waves are known as the sleep phases. Asernisky and Kleitman observed that normal, healthy sleep is divided into two main phases:

REM (Rapid Eye Movement) and NREM (Non-Rapid Eye Movement) [5]. REM sleep is also known as paradoxical or active sleep, which generally occurs about from 90 to 120 minutes during sleep in adults [6]. The remaining time of sleep is NREM sleep and night awakenings.

There has been reported recently that the sleep macrostructure is strongly associated with apnea episodes [7].

The most important signal for the classification of sleep stages is the electroencephalogram (EEG), one of signals recorded during polysomnography (PSG) [8]. It is used for distinguishing the wake and sleep phases [6]. The first EEG was recorded by Hans Berger. He was also the first

who observed the brain waves and described two of them: the alpha (8−14 Hz) and beta

M. Prucnal, A. G. Polak: EFFECT OF FEATURE EXTRACTION ON AUTOMATIC SLEEP …

(14−30 Hz) waves [9]. The other brain waves are delta (0.5−4 Hz), theta (4−8 Hz) and gamma

(30−80 Hz) ones [6]. Other brain activities, besides the waves, are artefacts like: saw-tooth waves, sleep spindles and K complexes [6].

Because of EEG signal complexity, the traditional manual sleep stage classification is time-consuming and depends on knowledge and experience of the expert. Therefore, an automatic

sleep stage classification is expected to be more objective, faster and more efficient. There are two approaches to scoring the sleep stages [6]. The first one follows the standardised scoring

systems introduced by Rechtschaffen and Kales [10], where the following phases are distinguished: wakefulness (W), rapid eye movement (REM), non-rapid eye movement (NREM) and movement time (MT). The NREM phase is additionally divided into light sleep (S1 and S2

stages) and deep sleep (S3 and S4 stages) [10]. Currently, a new method proposed by the American Academy of Sleep Medicine is used [1]. The main difference in stage definition is

that the S1-S4 stages are replaced by N1, N2 and N3 (joined S3 and S4) ones and the MT stage is no longer distinguished [1].

An automatic sleep stage classification usually takes the following steps: dataset preparation,

signal pre-processing, feature extraction and final classification [11, 12]. The dataset preparation includes splitting the EEG signal into 30-second epochs and organising subsets

of epochs from the same sleep stages: W, REM, N1, N2 and N3. The pre-processing consists mainly of filtering and normalisation of the signals. The crucial step is, however, the extraction of discriminative features form the prepared epochs, simultaneously reducing the number of

data for further processing. It is usually performed in the time, frequency or time-frequency/scale domains. Particularly the analyses in the frequency domain are very fruitful

[13, 14]. The time domain methods include statistical analyses [12, 15−20], the Hjorth approach

focused on activity, mobility and complexity [12, 16, 20, 21], and singular spectrum analysis (SSA) [22]. The methods in the frequency or time-frequency/scale domains describe the EEG

spectral or scale properties using the Fourier transform (FT) [11, 23, 24], power spectral density (PSD) [12, 25], short-time Fourier transform (STFT) [12, 26], adaptive directional time-frequency distribution (ADTFD) [27], Wigner-Ville distribution (WV) [12, 16], matching

pursuit (MP) [28], wavelet transform (WT) [12, 15, 16, 18, 29, 30], empirical mode

decomposition (EMD) [19, 31−35] or Hilbert-Huang transform (HHT) [36]. The methods most commonly used for classification are artificial neural networks (ANN) [11, 12, 15, 16, 18, 20,

23−25, 30, 32, 37], support vector machine (SVM) [12, 16, 17, 22, 23, 38], decision trees (DT) [16, 19, 33], random forest algorithm (RF) [12, 16, 29], and fuzzy systems [39].

The best reported accuracy of sleep stage classification exceeded 90%, e.g. 97.03% [16],

96.75% [40], 95.42% [18], 93.93% [41], 93.84% [42], 93.0% [15] and 90.11% [33]. In these works, the discriminative features were extracted using, among others, such methods as power

spectral density (PSD) [41], discrete wavelet transform (DWT) [15, 16], complex wavelet transform [18, 42] and empirical mode decomposition (EMD) [19, 33, 34]. Simultaneously, ANNs were used as classifiers in some of these approaches, e.g. [15, 16, 18, 40, 42].

It follows from the literature survey that often different classifiers of sleep stages were compared using only one feature extraction method [16, 19, 23]. There are only a few works

analysing combinations of some feature extractors and classifiers [22, 40], therefore comparing effects of the most promising feature extraction methods on the automatic sleep stage

classification results is desirable. For this reason, in this paper we examine three of such methods: power spectral density (PSD), discrete wavelet transform (DWT) and empirical mode decomposition (EMD) applied to signals from a single EEG channel, using a feedforward

multilayer neural network (FFNN) as the automatic sleep stage classifier.

230


2. Materials and methods

An automatic classification of sleep phases proposed in this work assumes the following steps: preparation of a database, signal pre-processing, feature extraction and final classification.

All the above processes were performed using MATLAB software (The MathWorks, USA).

2.1. Data

Data from the Sleep-EDF Database, available at the PhysioBank, were used. This dataset

contains polysomnographic (PSG) recordings from 10 healthy females and 10 males (25−34

years old) without any medication, registered during two subsequent day-night periods (about 20 hours in total each). One of these 40 records had been destroyed, so we have analysed all

remaining 39 files. The sleep recordings include signals from two EEG channels (Fpz-Cz and Pz-Oz) and the horizontal EEG, sampled with 100 Hz. All hypnograms were manually scored

by well-trained technicians according to the Rechtschaffen and Kales manual [10] (based, however, on Fpz-Cz/Pz-Oz instead of C4-A1/C3-A2 EEGs). The signals were divided into 30-second epochs and each epoch was assigned to one of the following sleep stages: W, S1, S2,

S3, S4 and REM. From these sets we selected 13650 epochs of a single Pz-Oz EEG channel (2730 epochs for each sleep stage) to prepare a maximally large and evenly distributed database.

Finally, the selected epochs were organized into 5 classes: W, N1, N2, N3 (combined S3 and S4) and REM, according to the AASM scoring system [1].

2.2. Signal pre-processing

At the beginning, the linear trend was removed from each of EEG epochs to eliminate the effect of a slow drift of electrode potential, amending the low frequency spectrum of a signal [44]. Then the epochs were normalised into a range between –1 and 1, aligning the energy

of signals coming from different subjects, electrodes and periods [44].

2.3. Feature extraction

The aim of feature extraction is to transform the 3000-sample epochs into much smaller, yet

still containing maximally discriminative information, vectors – i.e. into the feature vectors (FVs). The main idea of this work is to compare the three popular data processing methods used

for extraction of features from an EEG signal, which are: power spectral density, wavelet transform and empirical mode decomposition.

2.3.1. Power spectral density

Power spectral density (PSD) describes the distribution of average signal power in the frequency domain. The used Welch method is one of the most popular approaches to calculating

PSD from the fast Fourier transform [45]. It averages signal spectra from succeeding, overlapping time intervals, returning the estimate called a periodogram. In this work, the analysed epochs consisting of 3000 samples were split up into 512-sample segments,

overlapped by 50%, and then windowed using the Hanning window. As a result, 257 PSD values were received in a range from 0 Hz to 50 Hz with a resolution of approximately 0.19 Hz.

Admittedly, all the brain waves (delta, theta, alpha, beta and gamma) can be observed in each of the sleep stages, yet in a given stage some of them are dominant. Since the periodograms

characterising diverse sleep stages are different [6, 8], they can be used to generate discriminative features. The available frequency range of PSD was divided into five bands

231


corresponding to the five brain waves spectra. Power density in each of the bands was integrated

over three equal intervals (with midpoints at 0.59, 1.56, 2.54, 3.81, 5.37, 7.03, 8.69, 10.35, 12.11, 14.94, 18.95, 23.05, 29.20, 37.4 and 45.70 Hz), resulting in 15-element FVs characterising the analysed epochs.

2.3.2. Discrete wavelet transform

Discrete wavelet transform (DWT) enables the time-frequency (or time-scale) analysis of non-stationary signals and it is often used to study EEG [46]. This transform is similar to the

Fourier one, but it applies wavelets as the basic functions instead of sinusoids. A single wavelet, discretely sampled at n, is given in a general form as:

( )

⋅−=

j

j

jkj

knn

2

2

2

1

,

ψψ , (1)

where ψ is a wavelet prototype (or mother-wavelet). Wavelets are localised in time (a shift parameter k) and frequency (a scale parameter j), have a limited duration, zero mean and

normalised energy [46]. Using DWT, an original signal is decomposed by low-pass and high-pass filters, returning

appropriate signal components together with approximation coefficients a and detailed coefficients d for a given level, respectively. Then the low-frequency component can be further processed at the next level of decomposition. Finally, the signal x is decomposed into

a weighted sum of J-level series of basic wavelet functions ψ and a scaling function φ (covering all wavelets of higher levels) [15]:

( ) ( ) ( )∑∑∑ +=

= k

kJkJ

J

j k

kjkj nandnx,,

1

,,ϕψ . (2)

The sets of detailed coefficients Dj = dj,k and approximation coefficients AJ = aJ,k are then commonly used to create the FVs.

Practical application of DWT requires identification of an appropriate wavelet type, which should be similar to the analysed signal [15]. EEG signals are usually decomposed using the

Daubechies wavelets of order 2 or 4 [15, 16, 29, 47], so in this work the wavelet of order 3 (db3), particularly well resembling a local structure of this signal sampled with 100 Hz, has been applied. Additionally, it is necessary to determine the maximal level of decomposition,

depending on the required frequency range. Because EEG carries important information in a

range of 0.5−50 Hz, 5 levels of decomposition have been chosen, resulting in the following

frequency sub-bands: D1 (25−50 Hz), D2 (12.5−25 Hz), D3 (6.25−12.5 Hz), D4 (3.125−6.25 Hz),

D5 (1.5625−3.125 Hz), and A5 (0−1.5625).

The last step of extracting features using DWT is transforming the wavelet coefficients into

numbers. Finally, the average powers Pj of D1−D5 and A5 are calculated in each sub-band [15, 16, 18, 29, 30, 47], and expressed in dB (first six entries of the FV):

= ∑

=

jN

k

kj

j

j cN

P

1

2

,10

1log10 , (3)

where cj,k denotes dj,k or aJ,k, and Nj is the number of coefficients in the respective set at level j,

as well as standard deviations Sj of these coefficients [15, 16, 18, 47] (next six entries):

( )∑=

−

−

=

jN

k

jkj

j

j ccN

S

1

2

,1

1, (4)

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where cj are appropriate means. Although both Pj and Sj are proportional to epoch energy, this

energy is then such nonlinearly transformed, that Pj represents small differences between the features with higher resolution, improving the discriminative properties of the FV. Finally, each EEG epoch is represented by a 12-element vector of features extracted from the wavelet

decomposition.

2.3.3. Empirical mode decomposition

Empirical mode decomposition (EMD) is a method used in analysing nonlinear and

nonstationary signals, and it is often applied to EEGs [19, 31−35]. EMD is implemented as an

efficient iterative algorithm, which decomposes a signal into a finite number of non-parametric intrinsic mode functions (IMFs), having two properties [31]: 1) the number of extrema is the

same as the number of zero crossings (± 1); and 2) their envelopes are symmetrical in relation to the zero line. A signal x(t) after decomposition is represented as:

)()()(1

trtctxp

p

j

j∑=

+= , (5)

where: p is the number of IMFs depending on signal complexity; cj(t) are IMFs and rp(t) is the final residue. The iterative procedure is automatically terminated when either cj or rp are

negligible, or rp becomes a monotonic function. It is common to further apply the Hilbert transform to each of IMFs (the combined procedure

known as the Hilbert-Huang transform, HHT) to compute the instantaneous frequencies and amplitudes of these signals [36]. In this work, however, the FVs of the EEG epochs are calculated directly from IMFs as the average powers of IMFs expressed in dB (according to

(3)).

2.3.4. Alignment of feature vectors

Three methods used for feature extraction from EEG epochs were based on PSD, DWT and

EMD. They returned, however, feature vectors of different lengths: 15, 12 and 12−22, respectively. To objectively compare efficiency of these methods in classification of sleep

stages, the same classifier should be used, i.e. an ANN with a fixed structure, particularly with the same number of input neurons. Next, the principal component analysis (PCA) of the FVs obtained from PSD and EMD arranged as matrices was applied. This procedure transforms

orthogonally an original feature matrix F into a matrix S of linearly uncorrelated columns called the principal components, ordered according to the decreasing variabilities of data (related to

their discriminative abilities) [48]: S = FQ, (6)

where Q is a matrix constructed with eigenvectors of FTF. Finally, 12 first principal

components of the transformed PSD and EMD features were chosen for classification purposes, after standardisation of relevant Fs.

2.4. Classification

Artificial neural networks (ANNs) are widely applied to automatic classification of sleep

stages using an EEG signal [11, 15, 16, 18, 20, 23−25, 30, 32, 37]. They are popular for their high classification efficiency and relatively simple implementation [25]. A very important task

when creating an ANN is selecting a type and architecture of the network. Generally, an ANN consists of several layers of neurons: the input layer, one or more hidden layers and the output

layer. The numbers of hidden layers and neurons within them influence the ANN classification

233


capability [25]. It is known that an ANN with two hidden layers can approximate any

continuous mapping arbitrarily well. Also, most of classification problems can be solved by ANNs with only one hidden layer [25, 49].

In this paper, a feedforward neural network (FFNN) with the input layer consisting of 12

neurons (the size of FVs), two hidden layers with neurons characterised by a log-sigmoid transfer function and the output layer with 5 linear nodes (indicating the sleep stages: W, N1,

N2, N3, and REM) was used as the classifier. The optimal number of hidden neurons depends on the numbers of input and output neurons, the volume of training data and information covered by the data. It is common to determine it empirically. Thus, the FFNN structure was

selected by training FFNNs with different numbers of hidden neurons using the FVs obtained from PSD. Performance of each FFNN was assessed regarding the classification mean squared

error (MSE) and classification accuracy (a percentage of properly identified sleep phases) [25]. The whole procedure of classification was carried out in the following steps. For the three

examined feature extraction methods, the training, validation and testing sets were prepared by

randomly selecting feature vectors in a proportion of 70%, 15% and 15%, respectively. In each of these sets, the classes were systematically mixed in the sequence: W, N1, N2, N3 and REM.

Next, the PSD and EMD feature vectors were reduced to 12 principal components applying the PCA procedure (validation and testing matrices F were transformed into S according to (6), using standardisation parameters and matrices Q computed from the training sets). To find the

optimal FFNN structure, the supervised training process with an increasing number of hidden neurons (until 10 consecutive MSEs were larger than the smallest one) was performed by the

Levenberg-Marquardt algorithm, using the PSD features. It began with a random initialisation of neurons’ biases and weights [25], and took into account the validation set. In each case this process was restarted 30 times to increase the chance of finding the global minimum. The best

FFNN structure (returning the minimal MSE), found using the PSD data, was then used also for classifications based on the features obtained from DWT and EMD, repeating the training

procedure with 30 random initialisations. Such an approach enabled to show the differences in discriminative potential of the three examined methods of feature extraction from EEG

epochs.

3. Results

To analyse the feature extraction methods, 13650 30-second epochs of an EEG signal,

suitable for this work and assigned by the experts to 5 sleep stages, were finally extracted from the PhysioNet database, with the same number of elements in each class (2730 epochs). These data were evenly and randomly divided into the training (9100 epochs), validation and testing

sets (2275 epochs each). PSD was used as the first feature extraction method of calculating the average signal power

in 15 frequency intervals. The resulting feature vectors representing the N1, N2, N3, and REM sleep stages from the testing set (before PCA) are shown in Fig. 1.

The second method to concisely characterise the EEG epochs was DWT. According to the

characteristic spectrum of EEG signal sampled with 100 Hz, 5 levels of decomposition were chosen, resulting in 6 vectors of detailed and approximation coefficients for each EEG epoch

(Fig. 2), recalculated then into average powers and standard deviations. Similarly, all EEG epochs were processed by EMD, returning from 12 to 22 intrinsic mode

functions (Fig. 3), and then averaged powers and standard deviations were calculated from these

components. The next step of the study, where FFNNs with different numbers of neurons in two hidden

layers were trained using the 12-element feature vectors obtained from PSD and PCA, yielded the optimal structure of this classifier, i.e. the FFNN with 23+22 hidden neurons (Fig. 4a),

234


characterised by the minimal MSE (0.0567) and the classification accuracy of 81.1% (Fig. 4b).

FFNNs with the same optimal architecture were further used to test the efficiency of sleep stage classification based on the features extracted from the EEG epochs also by DWT and EMD. The final results are summarised in Table 1.

Fig. 1. Original features extracted by PSD for: N1(a); N2 (b); N3 (c) and REM sleep stages (d).

Fig. 2. Approximation and detailed coefficients from DWT (db3 wavelet) of an EEG epoch representing

the REM sleep stage.

235


Fig. 3. Intrinsic mode functions (from 3 to 8 of 18 IMFs ) derived by EMD from an EEG epoch

representing the REM sleep stage.

a)

Fig. 4. The optimal structure of classifier –FFNN with 23+22 neurons in the hidden layers (a);

dependencies of MSE and classification accuracy on the number of hidden neurons for the testing set

(the best results from repetitions of training restarted 30 times) (b).

Table 1. Accuracy of sleep stage classification using the FFNN with 23+22 hidden neurons

and the feature vectors extracted from EEG epochs by PSD, DWT and EMD.

Data Classification accuracy (%)

PSD DWT EMD

Training set 81.2 74.2 58.7

Testing set 81.1 74.2 57.6

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4. Discussion

The aim of this work was to compare the feature extraction efficiency of three methods: PSD, DWT and EMD in the automatic classification of sleep stages with the use of an ANN as the

classifier. The feature vectors extracted from PSD of N1, N2, N3 and REM sleep stages are shown

in Fig. 1. A pretty wide dispersion of values for particular features can be observed within a single sleep stage and similarities between FVs of N1 and REM, as well as FVs of N2 and N3. The differences represent the inter-subject variability following the fact that the analysed

epochs are obtained from two all-night EEGs of 20 subjects (10 females and 10 males). The widest dispersion of averaged powers can be observed during the N1 stage. This is possible

because N1 is the first stage of sleep, accompanying the process of falling asleep. N2 and N3

sleep stages characterise slow-wave sleep in which the delta waves (0.5−4 Hz) dominate, but

there are also the theta waves (4−8 Hz) during the N2 stage – the longest part of sleep. The similarity between the N1 and REM stages is caused by a large variety of frequencies within

them. Nevertheless, during the N1 stage the highest amplitude is in a range of 2−7 Hz. An example of approximation and detailed coefficients from DWT of one EEG epoch is

shown in Fig. 2. In this work, the EEG signal is transformed using the Daubechies wavelets

of order 3 (db3) at 5 levels of decomposition. In the literature, the Daubechies wavelets of order 2 [15, 29, 47] or 4 [16] were often used. Moreover, they were analysed for 4 [47] to 7 levels

[15]. An additional difference is that usually FVs were prepared using far more features, such as: energy of coefficients in selected sub-bands, total energy, ratio of different energy values, or standard deviation and mean of the absolute values of coefficients in each sub-band [15, 47].

In the work [29] also 5 levels of DWT were used, but the coefficients were transformed into a more rich FV by computing their variance, skewness and kurtosis.

Figure 3 presents intrinsic mode functions (from 3 to 8 of 18 IMFs in this case) derived by EMD from one EEG epoch. In this work, the FVs are created by calculating only average powers and standard deviations from all IMFs for each epoch, and then selecting the first 12

principal components using the PCA procedure. Because EMD yields different numbers of IMFs for different epochs, preselected quantities of IMFs are used in the literature to produce

larger feature vectors. For example, the features based on statistical moments (mean, variance, skewness and kurtosis) were calculated from the first 4 IMFs [19], and from the first 7 IMFs [34].

The optimal structure of FFNN for the PSD feature vectors with 12 neurons in the input layer, 23 + 22 neurons in two hidden layers, and 5 neurons in the output layer has been found

in this work (Fig. 4a). In the literature, other structures of FFNN for the PSD FVs were used. For example, a network with 30 input neurons (PSD for 30 spectral bands from 0.5 Hz to 30 Hz), 6 output neurons (W, S1, S2, S3, S4 and REM) and 11 neurons in one hidden layer revealed

a classification accuracy of 76.7%, and an ANN with 4 output neurons (W, S1/S2, S3/S4 and REM) and 7+7 neurons in two hidden layers demonstrated a classification accuracy of 81.5%

[25]. Hsu et al. [11] proposed an FFNN with 6 input neurons, 6 neurons in one hidden layer and 5 output neurons with a classification accuracy of 81.1% as the optimal structure from the three

types of neuron classifiers: Elman Recurrent ANN, FFNN and Probabilistic ANN. In another work, a structure with 15 input neurons, 32 neurons in the hidden layer and 3 output neurons (alert, drowsy and sleep) was chosen, returning accuracies over 92% [47]. That work, however,

was not focused on the classification of sleep phases. The final classification results are presented in Table 1. The best accuracy (81.1% for the

testing set) is obtained for extracting the features from EEG epochs by PSD and then calculating averaged powers in 15 sub-bands related to the brain waves spectra. This result is comparable to the former works using ANNs [11, 25]. The primary difference between the used feature

237


extraction methods based on PSD, DWT and EMD is that the first one takes directly into

account the bounds of spectra of the brain waves, and the other two do not. Achieving higher accuracy for 5 classes using only the EEG signal is very difficult, because of the similarities between the N1 and REM, and the N2 and N3 sleep stages (compare Fig. 1). This is due to the

fact that PSD presents information about the average spectral nature of signal in 30-second epochs. The classification results obtained with DWT could be probably better if the FVs were

extended by either such features like energy of coefficients [15, 47] or statistical features: mean, variance, skewness and kurtosis [29], or by using DWT with the Daubechies wavelets of order other than 3 [16]. Especially the approach combining the decomposition coefficients related to

the specific brain wave bounds seems to be very promising [15]. A classification accuracy with FVs from EMD is surprisingly low (57.6%). Moreover, this approach is computationally less

efficient due to an iterative procedure of finding the intrinsic mode functions. Probably better results can be achieved if the Hilbert transform is applied to IMFs (the Hilbert-Huang Transform [31]) and then specific frequency sub-bands are selected to produce features [36], or

if the statistical features of the IMFs are also taken into account [19, 34]. The best reported results of sleep stage classification from an EEG signal (e.g. [16, 18, 41, 42]) used mixed signals

or methods of feature extraction and larger FVs, but such approaches are beyond the scope of this paper.

5. Conclusion

Three methods of feature extraction from EEG epochs: power spectral density, discrete wavelet transform and empirical mode decomposition, were tested for the purpose of sleep stage classification by artificial neural networks with the same structure. The best result,

characterised by a classification accuracy of 81.1%, was yielded when the features were prepared using averaged powers from the frequency sub-bands of PSD and a feedforward neural

network with 12 input neurons, 23 + 22 hidden neurons and 5 output neurons was applied as the classifier. Such an outcome shows that the efficiency of PSD is better than DWT and EMD

in this specific classification problem. Also, it stresses the importance of using the frequency sub-bands characteristic for the brain waves to detect the sleep stages from EEG.

Although this preliminary study has unambiguously shown that PSD returns the best results

in comparison with other tested methods of feature extraction, it is worth to continue this study focusing on some selected issues. First of all, a possibility of extracting the characteristic

frequency sub-bands from DWT (by combining selected approximation and detailed coefficients) and EMD (by using the Hilbert transform) should be tested. Also, computing larger sets of features within these approaches to EEG processing, besides average powers and

standard deviations used in this work, can be tried. And finally, other classification methods, e.g. the support vector machine or decision trees, may suit better dealing with this particular

problem. Analysing all the above possibilities should lead to obtaining even better classification accuracy than that achieved in this study.

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Article history: received on Oct. 14, 2016; accepted on Jan. 14, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0026.


Index 330930, ISSN 0860-8229


INTERFEROMETRIC SET-UP FOR MEASURING THERMAL DEFORMATIONS OF PRECISION CONSTRUCTION ELEMENTS Marek Dobosz, Mariusz Kożuchowski, Marek Ściuba, Olga Iwasińska-Kowalska, Adam Woźniak Warsaw University of Technology, Faculty of Mechatronics, Św. A. Boboli 8, 02-525 Warsaw, Poland ([email protected], [email protected], [email protected], [email protected], [email protected], +48 22 234 7665)

Abstract

Many precision devices, especially measuring devices, must maintain their technical parameters in variable

ambient conditions, particularly at varying temperatures. Examples of such devices may be super precise balances

that must keep stability and accuracy of the readings in varying ambient temperatures. Due to that fact, there is

a problem of measuring the impact of temperature changes, mainly on geometrical dimensions of fundamental constructional elements of these devices. In the paper a new system for measuring micro-displacements of chosen

points of a constructional element of balance with a resolution of single nanometres and accuracy at a level

of fractions of micrometres has been proposed.

Keywords: interferometric measurements, thermal deformations, precise balance.


1. Introduction

Many precision devices, especially measuring devices, must maintain their technical

parameters in variable ambient conditions, particularly at varying temperatures. An example of such a device may be a super precise balance produced by Radwag [1]. This device must

keep stability and accuracy of its readings in varying ambient temperatures. Due to that fact, there is a problem of measuring the impact of temperature changes, mainly on geometrical dimensions of the device’s fundamental constructional elements. An assumption was made that

precise balances should operate in air-conditioned laboratory conditions, where the ambient temperature is kept equal to approximately 20ºC and allowed changes in temperature can be

very slow (e.g. 1ºC/h). Due to the size of construction parts that ranges from single to several centimetres, we had to be prepared for dimensional changes ranging from fractions to single micrometres. This meant the necessity to develop a system for measuring micro-displacements

of chosen points of a balance constructional element with a resolution of single nanometres and accuracy at a level of fractions of micrometres. In order to analyse the impact of temperature

changes on the geometrical changes of elements, a need emerged for setting the temperature changes with high accuracy and stability (at a level of 0.01ºC per 8 hours), while keeping

minimal (below 0.01ºC) gradients of temperature in the environment of a tested element. It could seem that the problem of setting the temperature changes of a tested element can be solved by using climatic chambers available on the market.

Typical temperature changes in the available climatic chambers which could possibly be used range from zero to tens of degrees. While the range of temperature changes exceeds the

required one, also accurate setting temperature and distributing it appropriately inside the chamber becomes a problem. It has been proved that typical accuracies of the set temperatures are about 0.1ºC with gradients inside the chamber reaching 0.2ºC [2]. This meant the necessity

M. Dobosz, M. Kożuchowski, et al.: INTERFEROMETRIC SET-UP FOR MEASURING THERMAL …

of developing a specialized research set-up including a chamber and a system for non-invasive

measurement of micro-displacements. In this paper we demonstrated a set-up with a temperature stability level in the chamber

reaching the value of 0.01ºC per 8 hours. This value is at least about one order of magnitude

better than that offered by commercially available climatic chambers. The described optical set-up in the chamber is able to measure components of various scale.

Most of the known solutions are designed to measure a thermal expansion coefficient of the

prepared block or tube samples [3−5] and gauge blocks [6]

2. Construction of appliance

The analysis of the problem has led to the following general concept of the measuring set-

up. It is composed of two basic units: a thermal chamber for setting controlled changes in temperature of a tested element and a laser interferometric system for measuring micro-

displacements of a chosen test element. Inside the chamber, there is a unit of the measuring interferometer. The tested element is placed on a base made of a material with almost zero thermal expansion coefficient.

2.1. Thermal chamber for setting changes and stabilizing ambient temperature The purpose of the chamber is to stabilize air temperature at a level of 0.01ºC per 8 hours

in the points ranging from 15 to 35ºC, chosen by the operator. In the stabilized area, long-term

interferometric measurements are to be performed, thus the level of temperature stability is the main parameter of the set-up. Therefore, when developing the concept and construction of the

chamber, the greatest emphasis has been put on the elements affecting the level of obtained

temperature stability, then − on the dynamics of changes between thermal points set by the operator.

Chamber assembly and its power supply

Precise setting of temperature in a volume not exceeding 0.5 m3 requires extremely precise

control of the heat flow. Thus, semiconductor Peltier modules were applied as a thermal pump,

which − due to a close relationship between the current and supply voltage and the efficiency

of heating and cooling − enables precise controlling the heat conveyor. In the chamber there are to be performed long-term measurements of the dimensional stability of metal elements with

the use of interferometric technique. As the target level of uncertainty of these measurements is expected to be several to several dozen nanometres, it was crucial to minimize temperature

gradients in the stabilized space, as well as to reduce mechanical vibrations caused by the system of temperature stabilization. These vibrations would affect the readings of the interferometric system. In order to minimize mechanical vibrations, two technical solutions

were applied. First, the chamber was put on a special table, the top of which floats on airbags and its construction is optimized with the use of vibro-insulation.

Secondly, the system has been divided into two parts: the chamber and a separate system of setting changes and stabilization of temperature. The temperature in the chamber is set with the use of a water jacket surrounding all walls of the chamber. The water jacket is made

of flexible plastic tubes transporting liquid of a predetermined temperature. The applied water jacket surrounding the entire chamber separates the stabilized area from external conditions.

Additionally, it ensures a proportional distribution of heating and cooling of the entire volume of the chamber, what minimizes thermal gradients and eliminates the need for forced (e.g. by ventilators) air mixing. The water jacket is supplied with water from a tank located on a rack

not mechanically connected with the chamber. In the tank, the temperature of water is stabilized and then provided to the chamber by flexible hoses. Thanks to the separating the chamber from

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the system controlling temperature, vibrations of the necessary ventilators responsible for heat

removal from cooling/heating elements (peltiers) of the electronic system are not transferred into the thermal chamber.

A schematic diagram of the appliance is presented in Fig. 1. The climatic chamber (1) is

placed on an optical table (2), characterized by a high mechanical stability due to using the honeycomb structure in its interior. The whole is supported by vibro-insulation legs (3),

containing pneumatic systems levelling the table. The water jacket of the chamber is supplied with water from a tank (4) with a capacity of about 25 litres. It is covered by a 5 cm layer of styrodur (5) separating the stabilized liquid from influence of the ambient temperature. The

liquid is transported to the chamber through flexible hoses, its circulation is forced by a set of pumps (6). Change of temperature in the tank is controlled by Peltier modules (7), which are

put between two water blocks acting as heat-exchangers between the liquid and the surface of the modules. Heat flows between the hydraulic circuit of the chamber and the system supplying or receiving heat from Peltier modules. This system consists of pumps (8) and an air

cooling system (9), the efficiency of which was improved by adding ventilators forcing the air flow. At the highest point of the system surge tanks are located (10), the task of which is to

maintain an adequate level of liquid and to compensate its thermal expansion. An electronic module (11) is responsible for controlling the Peltier module.

Fig. 1. A schematic diagram of the set-up for temperature stabilization in the chamber with an interferometer.

Chamber construction

In order to obtain a stable temperature in the chamber without the necessity of additional air

mixing, we decided to create a water jacket, which surrounds the stabilized space. There were used specialised synthetic hoses, with their construction optimized by reducing internal wall

roughness and increasing a bending radius. It influenced the resistance of liquid flow and enabled to avoid folding a hose when putting it in the walls of the chamber. Since the total length of the hydraulic circuit in the chamber is 45 meters, reducing the flow resistance was

crucial for obtaining an appropriate capacity of the system when using pumps which − while

ensuring negligible pressure (and vibration) fluctuations − were characterized by an insignificant pressure.

The structure of the wall and chamber base is presented in Fig. 2. Hoses (2) were squeezed between the inner wall of the chamber (1) and the intermediate wall (4). This was made in order to increase the contact surface of the hoses with the chamber walls, making the flow of heat

more efficient. Moreover, the chamber had to be made of non-magnetic elements. Sheet metal was good heat exchanger with the interior of the chamber and at the same time distributed heat

evenly. The hose system was separated from the surroundings with a layer of foamed

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polystyrene (3) to reduce a power loss in the system stabilizing the liquid temperature.

The whole was surrounded by painted stainless metal sheet (5).

Fig. 2. The structure of the thermal chamber’s wall.

The base of the chamber was integrated with the optical table equipped with threaded holes. They enabled pulling the hoses to the top of the table, which thus was thermally stabilized, just like the interior of the chamber. This was a barrier to the influence of ambient temperature on

the chamber’s space. Additionally, the thermal stabilization of the top of the table improved the mechanical stability between the measured elements in the chamber and the located outside the

chamber elements of measuring interferometer, which was mechanically linked to the top of the table. In one of the side walls of the chamber, two electric passes were made with cable connectors for insulation and an optical hole enabling to introduce a laser beam of the

interferometer into the chamber. The assembled chamber is presented in Fig. 3.

Fig. 3. A view of the chamber together with the table and elements of interferometer.

2.2. Measuring base

In order to enable thermal measurements of the changes of geometrical dimensions of small elements, it was necessary to solve the issue of thermal expansion of the base to which a tested

element was attached. The theoretical analysis of the problem proved that, in general, the only solution was the application of a measuring base made of material of a negligibly small coefficient of thermal expansion. Such materials are special optical glasses, from among which

we selected ZERODUR glass manufactured by the Schott company. The coefficient of thermal

expansion of this glass in the described application can be regarded as zero (α = 0.1∙10−6 K−1

[7]). We ordered a ZERODUR plate of the following dimensions: 140 × 260 mm2 and

a thickness of 25 mm. It is used as a measuring base, on which we place elements which geometrical changes caused by temperature changes are measured.

Inside the chamber there is a table (Fig. 4) supported by 3 legs screwed into the top of the optical table. The legs are equipped with cermet balls, that penetrate into appropriate sockets

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in the base of the table. The result is more repeatable attachment of the table to the chamber

and the measuring system, as well as a reduced heat flow between the table legs and the table itself. The base of the table is made of an aluminium plate, with the previously mentioned glass base plate put on it.

Fig. 4. A view of the chamber together with the table and elements of interferometer.

2.3. Construction of system of temperature stabilization

General concept and mechanical assemblies

Setting temperatures in the chamber is possible due to the application of Peltier modules as bi-directional heat pumps. Four Peltier modules were used with a total, maximum cooling

capacity of 350 W and a heating power of 1000 W. Such a disproportion results from the efficiency of the mentioned modules. In order to receive power from the modules, they were placed between water blocks (Fig. 5). A water block consists of a copper element, its flat side

adjacent to the module and the other one ribbed specifically in order to increase the contact between the metal surface and the flowing water. The stream of liquid is directed into the ribs

of the copper element by a system of channels in the housing of the water block made of a temperature- resistant synthetic material .

Fig. 5. A Peltier module between water blocks.

The liquid in hydraulic circuits is distilled water with addition of inhibitors, which aim is to stop or significantly slow down the reactions between the components of hydraulic circuit made

of different metals. Distilled water provides a very good thermal conductivity while being neutral to the environment and the operator, as the stabilization tank is not hermetically sealed in order to compensate for the thermal expansion of the liquid.

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A hydraulic circuit responsible for exchanging heat from Peltier modules with the

environment is presented in Fig. 6. In the bottom part, above the tank, where the liquid for the chamber is being prepared, four pumps are located. Each Peltier module has an individual hydraulic circuit. The use of the same models of elements in each circuit provides a similar

cooling capacity, flow and temperature. The pumps has been placed at the lowest point of hydraulic circuit so as to be influenced by a possibly high static pressure. These pumps

provide a stable flow with no significant pressure fluctuations. The pumps send liquid directly into water blocks of the Peltier modules, which then goes to the highest points of the circuit tanks. Plexiglas expansion tanks enable to control the liquid level and to pick up gas bubbles

emerging in the liquid. They also have an internal dividing wall with its inside dimension a few times larger than the diameter of hoses supplying liquid. It slows down the speed of water flow

what enables to surface the bubbles and to eliminate them from the hydraulic circuit. The surge tank liquid is transported to a set of radiators. They are made of copper in order to increase the heat flow efficiency. Each radiator is equipped with four ventilators. Two of them inject air into

the radiator and the other two suck it out from the other side. As a result, the efficiency of the radiators has been improved several times. It is highly important because of the Peltier modules’

properties. Their maximum cooling power is inversely proportional to the generated difference of temperatures between their ceramic covers. The higher the temperature difference, the lower the efficiency of the module. This means that the more effectively the heat is received and the

warm side of the module is cooled down, the lower temperature can be achieved on the cool side.

Fig. 6. A hydraulic circuit of the heat exchanger.

Electronic control - temperature regulator

As already mentioned, the air temperature regulator in the measuring chamber is based on the stabilization of temperature of the liquid flowing through the walls of the chamber. Adjusting the temperature of the liquid assures a higher stability of temperature and its more

precise regulation (related to a heat capacity of the unit). The electronic system controlling temperature stability has been divided into the following blocks:

− the main controller;

− controllers of power stages;

− temperature measurement systems;

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− a power supply. The main controller is a system controlling particular modules and is responsible for:

− communication with the control master computer (setting temperature changes, sending the results of measurement to the master computer, determining the operation mode);

− communication with temperature sensors (through intermediate processors used because of the necessity of changes in the transmission protocol, as well as for reducing the distance between processor and sensor);

− implementation of an algorithm of temperature regulation;

− controlling power stages (regulation of the level of heating/cooling);

− controlling correctness of the system operation. The power controllers are systems supplying Peltier modules which enable:

− regulation of the power supply of the module (and the related efficiency);

− switching between the heating/cooling functions. The temperature measurement is carried out with the use of integrated semiconductor

thermometers of ADT7320 type with a high measuring accuracy (0.2ºC guaranteed with no

additional calibration, 0.002ºC typical accuracy and repeatability better than 0.02ºC). Thus, such systems are equipped with an SPI interface and an additional microcontroller located near

the thermometers, applied to control the measurement and to send the results to the main controller via an RS485 interface. Separating the microcontroller from the temperature sensor is necessary to reduce the influence of heating of the microcontroller on the measurement.

Communication of the main controller with other modules is made on the basis of an RS485 interface (two channels). It enables a two-way transmission between multiple systems with the

use of two wires. If necessary, it makes possible adding other systems without a need of rewiring.

The entire system is supplied from a 24V 1000 W chopper power supply. Each plate has local stabilizers generating voltage necessary for the operation of each module. The power control modules need 190 W each when fully controlled. Other systems take approximately

3−4 W. The main controller is made on the basis of an ATMega64 microcontroller. Additionally, it

has two UART hardware systems that are used for transmission to sub-systems. UART

conversion systems − RS485 (SN75176) and USB-FT245 bridge are located in the surroundings of the microcontroller. SN75176 (U4 and U5) systems convert TTL level signals (RxD and TxD of the processor) into differential signals required for the RS485 transmission. Since it is

two-way transmission, a signal of choosing the transmission direction is required. In order to ensure correctness of the transmission and protect it against a possibility of simultaneous

transmission through different systems, the receiver module is still on and the microcontroller is able to view the signal on the main line. If the received signal is in accordance with the sent one, the transmission is correct.

To communicate with the master computer, an FT245 (USB converter) system has been used. This system is seen as a serial port, what simplifies the control (it is possible to use the

terminal for sending and receiving data). An LCD display is used for indicating a current condition of the processor and peripheral

systems. It enables to display current settings of temperature, the results of its measurement and to signal whether the system is currently in a heating or cooling mode.

The system of power supply and control of the Peltier modules has been made in the form

of four identical control modules. These modules enable independent controlling any voltage of any polarization (as regards the voltage of Peltier cells operation) of one of the four cells.

The adjustable power supply is a pulse converter lowering the supply voltage (24 V) to the

voltage required by a Peltier cell (0−16 V) at the required load current equal to 10 A. The converter is controlled by PWM signals from the outlets of the processor. The PWM signals

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are provided to the inputs of the controller system of IR2113 transistor half-bridge, which gives

a current output sufficient to drive the power transistors. A frequency of PWM is 55 kHZ. The PWM is operated on 55% and 35% cooling and heating duty cycles, respectively. These values were determined to achieve similar speeds of heating and cooling.

At the same time, this driver provides voltage higher than the power supply voltage, what is required for correct operation of the keying transistor. As the module must provide a change

of polarization of the output voltage that is required to switch between the heating and cooling modes, it was inevitable to use an H-bridge for producing the switching voltage.

To reduce the influence of other elements on the temperature sensors (especially when

heating), the systems were located on the plates only with elements reducing interference. In order to provide a good heat exchange with the environment, the elements were assembled

on the aluminium base. As thermometer systems are equipped with an SPI interface, it becomes necessary to use an

intermediate microprocessor system between the thermometer and the main controller module.

This intermediate system is based on an ATMega8 microcontroller. It provides control of 4 digital thermometers, as well as communication with the control module via an RS485

interface. The microcontroller controls the thermometer system in such a way that temperature

measurements are made at intervals of 1 second, with the maximum resolution of thermometers.

Between the measurements the systems are put to sleep, what reduces the heating of thermometers.

3. Measurement of micro-displacements

3.1. Assumptions for construction of specialized interferometer

Measurement of the geometrical changes of mechanical parts having dimensions starting from a few centimetres at a change of temperature to 10ºC requires providing a measurement

resolution of displacements of a nanometre level. In practice, this means the need for applying an interference method.

Because of testing the influence of ambient temperature on an examined element, we were

not able to use incremental or contactless encoders, which would require placing a detector in the thermal chamber. Due to that fact, we suggested a solution in the form of a laser

interferometer, where a laser beam would be brought to the thermal chamber from the outside. Assuming the use of a conventional interferometer with a reflector operating in one of its

arms for measuring displacements of often quite flexible mechanical elements of the balances,

it was necessary to adopt the following assumptions:

− minimization of weight, and thus a size of the measuring reflector together with its fastening, what leads to:

− inability to precisely adjust the position of the reflector towards the laser beam (an accuracy

of linear − in the order of 0.3 mm, and angular positioning – in the order of 1º). Taking the above into consideration, it was necessary to use a cube corner prism of possibly

small weight and small dimensions as the measuring reflector. It resulted in another problem − commercially available prisms having such small dimensions are characterized by low accuracy (non-parallelism of the outgoing beam to the incoming beam is approx. 15ˮ). This means that

conventional reading systems of interferometers designed to operate with prisms of 2ˮ accuracy are not suitable for use in this case. That is why it was necessary to apply a special receiving

system of interference fringes which would give a correct reception of a signal disturbed as a result of the non-parallelism of interfering beams.

248


The above mentioned problems led to the need of developing from scratch a specialised laser

interferometer which could operate according to the principle of counting interference fringes.

3.2. Description of construction

Laser

When constructing the interferometer, we assumed the use of a single-frequency He-Ne laser-based interferometer. The rationale is a simple construction providing significantly lower costs of construction and the possibility of greater miniaturization of the measuring system,

while homodyne are similar to heterodyne systems in terms of their metrological parameters. The final argument for selecting this type of solution was adopting the concept of a receiving

system insensitive to the interference angle, which, by definition, cannot operate on high frequencies of signals.

Due to a variable difference in optical paths, which may occur when measuring elements

of different dimensions, it was indispensable to use a stabilized He-Ne laser. A requirement was formulated that the uncertainty of determination of light wavelength is at a level of 0.001 nm

what gives a relative measurement error of displacement coming from this source at a level

of 1.5 ∙ 10−6 nm. Such a value is entirely sufficient due to a small range of the measured displacements. As an example, when measuring changes in the dimensions of elements of the

order of 10 µm, this component of uncertainty will generate a negligible error of 1.5 ∙ 10−2 nm. A two-frequency Thorlabs HRS015 laser has been used. In the further described system,

only one mode was used.

General configuration of interferometer

A general scheme of the interferometer with particular subassemblies, is presented in Fig. 7.

Fig. 7. A general scheme of the interferometer construction.

At the beginning, from the beam of the two-frequency He-Ne laser, one frequency of linear polarization is separated with the use of a polarizer P1. In the next stage the beam is expanded

to a diameter of 2 mm adjusted to dimensions of the applied cube corner reflectors. A collimation telescope K1 is used for this purpose. Next, the beam passes through a quarter-wave plate QR, which transforms the linear polarization into the circular polarization being an

effect of putting together two linear disturbances which are mutually perpendicular and phase-shifted by 1/4 of a light wavelength. The such prepared beam is emitted outside the laser head

towards the interferometer assembly. This beam is directed via prisms/mirrors M1 and M2 to a polarizing cube beam-splitter BS. The mirror M1 directs the beam perpendicularly to the Zerodur base surface. The prism M2 cemented with the beam-splitting element is moved along

the axis of the beam behind the mirror M1 enabling the interferometer to operate at different heights depending on the height of measured detail. A reference cube corner reflector RCCR

is cemented to one side of the cube beam-splitter. It has identical dimensions as the measuring cube corner reflector MCCR. Due to that fact, changes in temperature in the chamber change

P1

K1QR

K2

M1

M2BS

RS

Zerodur

M3M4

RCCR

MCCR

249


the optical paths in both cube corners in the same way, without generating an error significant

for the measurement. The polarizing cube beam-splitter directs a component of type P light polarization to the referential prism and then, after reflecting the beam, directs it back to the

laser head. A type S polarization component is transmitted through the beam-splitting layer to the measuring cube corner reflector which is glued to the tested surface for the time

of measurement. The reflector directs the beam back to the beam-splitter, which − after passing

through it − returns to the laser head. Both beams are at the beginning introduced into the laser telescope K2, which expands them to a diameter of approx. 4 mm. adjusted to the receiving photo-detection system RS.

Specialized photo-detection system

There are two main types of receiving systems of interferometer: (i) photo-detective systems

operating with zones of interference fringes of an infinite period [8] (classic solution) and (ii) systems operating with fringes of a finite period [9].

As already mentioned, due to insufficient angular accuracy of the cube corner reflector-

prisms applied in the system of interferometer it was not possible to apply a classic photo-detection system because of a finite and unstable (dependent on the settings of the reflector)

period of the fringes. This problem has been solved by applying a special photo-detection system based on a patent [10] and developed in the Institute of Metrology and Biomedical

Engineering within an earlier research project and presented in detail in [11]. The receiving system is composed of the following elements:

− birefringent wedge;

− polarizer;

− cylindrical lens;

− photodetector. The adopted receiving system is presented in Fig. 8. When passing through the birefringent

wedge W the measuring and reference beams MB and RB, respectively, having mutually perpendicular linear polarization, are refracted at different angles dependent on their own

polarization. This is a result of different values of the refractive index of ordinary and extraordinary rays. The wedge is made of birefringent crystal and the refraction angle depends

on the wedge direction and the angle of its cut, so behind the wedge the beams run at some non-zero angles. The wedge itself must be able to rotate in order to be regulated. Next, the set P2 polarizer brings the measuring and referential beams to the common surface in order to enable

their interference. The cylindrical lens CL together with properly designed regulation of the photodetector P position enable adjusting the area of interference to the surface of the

photodetector.

Fig. 8. A chart of the receiving system of interferometer.

Assembly of polarizing beam-splitter

The purpose of the polarizing beam-splitter assembly is precise introduction of the laser beam into the cube corner reflector placed on the tested element surface. Its construction must

eliminate the influence of temperature changes on the result of measurement. A possibility of precise adjustment and fastening of the system on the measuring table is equally important

as regulation of height at which the cube beam-splitter is set. These conditions are fulfilled by a mechano-optical system, a diagram of which is presented in Fig. 9. The assembly

of interferometer beam-splitter is composed of three optical elements cemented together:

250


a rectangular prism M2 directing the beam, a polarization cube beam-splitter BS dividing the

beam and a reference cube corner reflector RCCR. This assembly is mounted to a carriage, which is able to move along a slide perpendicular to the Zerodur base surface. It enables to run the measurement beam both parallel to the Zerodur base and at the desired height determined

by the tested element size. The height of cube and prisms is precisely regulated by a micrometre screw

After adjusting the desired height the assembly can be stiffly fixed. Locking the assembly position by a bolt is supposed to guarantee mechanical stability of the beam splitting assembly during measurements. It was extremely important to design a stable attachment of the assembly

and the tested detail together with the corner mirror to the Zerodur plate. The point of reference which has to be provided with a possibility to keep an unchanged position is the assembly

of beam-splitter together with the reference reflector. Even a slight thermal change of the position of this reference assembly may significantly affect the result of measurement. Thus, in the project of assembly construction two support surfaces were made, located symmetrically

to the cube, situated in the same vertical line as its centre. The shape and dimensions of the beam splitting element provides minimal influence

of thermal deformations on the result of measurements. Fastening the assembly to the base plate may be carried out by pressing the whole assembly to the Zerodur base in such a way that the points of pressure are located symmetrically on both sides of the cube beam-splitter. However,

in the majority of measurements, the assembly was stuck to the base with the use of some protruding surfaces located symmetrically in relation to the referential prism.

Fig. 9. A schematic diagram of the interferometer beam-splitter assembly.

Measuring reflector

The construction of measuring reflector is based on the use of a cube corner prism with dimensions enabling to work with a laser beam with a diameter of approx. 2 mm. In the project

we have used an Edmund Optics corner prism with an outer diameter of 7.16 mm, what enabled

to keep an optimal size of the housing with the following dimensions: 8 × 8 × 6.3 mm3. The housing of cube reflector make it possible to be mounted in various arrangements (Fig. 10).

On the external surfaces of the housing there are made outlets, one of which located on the axis of the tip of the prism can be glued at the desired point of the part, the displacements

of which are to be measured. The assembly weighs about 0.8 g. An atempt was made to reduce mass of the optical element in order to decrease the influence of weight on the geometry of the measuring part. Small dimensions are required to limit the mounting area.

Attaching element to base

On each tested element two points are determined − the first, a reference point towards which geometrical changes of the detail are measured, and the second, a measuring point to which the

measuring reflector of interferometer is attached. Depending on the position of base point on the part, additional intermediate elements are used. Fig. 11 a shows a fragment of the part with a hole the axis of which acts as the base point. In this case, attaching to the surface at this point

was carried out with the use of a screw stuck by a conical head to the Zerodur surface and

251


pressing the measured element by a conical nut, as shown in Fig. 11b. Depending on a form

of the reference point, various specifically designed intermediate elements were used.

a) b)

Fig. 10. A simplified design drawing of the assembly of a measuring cube corner reflector (a);

a view of mounting of the measuring reflector to a tested part (b).

a) b)

Fig. 11. Attaching the reference point to the Zerodur base surface. A fragment of construction drawing

of the tested part (a); a view of a cone nut clamping the element to the base screw (b).

The place of sticking the screw to the base plate is here invisible.

4. Tests of appliance and discussion

The basis for evaluation of the feasibility of performing the necessary tests using the

developed appliance was verification of stability of the interferometer readings during changes of temperature in the chamber. In this case, the measuring reflector was glued with the use of its housing directly to the Zerodur base (the measured element was not used). A distance between

the measuring and reference reflectors was approximately 105 mm. Next, temperature in the chamber was periodically changed and the interferometer readings were saved. Two options

of data saving were used − without and with the numerical correction of light wavelength changes. The sensors of temperature, pressure and humidity installed in the chamber were used to evaluate the actual air refractive index and to calculate the actual wavelength basing on the

Edlen formula [12] and its subsequent amendments [13, 14]. An amplitude of changes in temperature was 9.5ºC. The test duration was 64 hours. Sample test results are presented

in Fig. 12. A purple line shows the applied temperature changes. A red line shows differences in the interferometer readings obtained without the wavelength correction. A green line shows the interferometer readings including the influence of environment on the air refractive index

(and the light wavelength).

252


a)

b)

Fig. 12. Changes of the readings of the position of measuring reflector caused by changes of temperature (a);

an enlarged part of the corrected readings (b).

When analysing the graph we can notice that in the first several hours of changing

temperature the response of interferometer is incorrect. It results from deformation of the

mechanical elements of interferometer under the influence of temperature gradients. However, after 10 hours of increasing temperature and after 8 hours of stabilization at a high level, the

readings of interferometer reach a level of systematic error of about −0.12 ÷ −0.11 µm. This

corresponds to the relative inaccuracy of measurement equal to approximately 10−6. When cooling the chamber, stable readings are achieved slightly earlier, after about 8 hours from the beginning of cooling and after 6 hours from the beginning of stabilization in the lower

temperature; the systematic error is at a level of about −0.1 ÷ −0.08 µm. This corresponds to

the relative inaccuracy of measurement equal to approximately 10−6. These are satisfactory values. However, obtaining this level of inaccuracy in practice requires approx. 8 hours for

temperature stabilization after its change. Unfortunately, it significantly extends the duration of measurements. The noise of interference signal is a result of fluctuations of the

253


interferometer indications caused by temperature gradients of the air in the chamber and

vibration of the set-up. This random noise does not exceed 10 nm with a signal resolution of 1 nm.

If the systematic error value exceeds the required value, the only way to solve the problem

is to carry out the measurement in a different way, i.e. with the use of a measured detail, and then without it, but with the same difference of optical paths.

The last horizontal section of the graph shows at the same time the achieved level of temperature stability in the chamber, which reaches a value of 0.01ºC per 8 hours. This value is at least about one order of magnitude better than in commercially available climatic

chambers. Summing up, the following technical parameters of the calibration system were obtained,

which were confirmed by the experimental test results:

− a relative inaccuracy of displacements’ measurement is equal to about of 10−6;

− a time interval required for stabilization of temperature (after a change of about 10ºC) in order to achieve the assumed uncertainty is approx. 8 hours;

− a level of temperature stabilization is of about 0.01ºC per 8 hours;

− a range of possible operating temperatures is equal to 15ºC−35ºC.

Acknowledgements

The research has been funded from the research budget for 2013-2016 as a research project

PBS2/B6/16/2013 of The National Centre for Research and Development of Poland.

References

[1] http://radwag.com/pl/

[2] http://www.binder-world.com/pl/Produkty/Komory-klimatyczne-do-test%C3%B3w-

stabilno%C5%9Bci/Seria-KBF/KBF-115#1

[3] Schödel, R. (2008). Ultra-high accuracy thermal expansion measurements with PTB’s precision

interferometer. Meas. Sci. Technol., 19. 084003, 11.

[4] James, J.D., Spittle, J.A., Brown, S.G.R., Evans, R.W. (2000). A review of measurement techniques for the

thermal expansion coefficient of metals and alloys at elevated temperatures. Meas. Sci. Technol., 12, R1–

R15.

[5] Cordero, J., Heinrich, T., Schuldt, T., Gohlke, M., Lucarelli, S., Weise, D., Johann, U., Braxmaier, C. (2009).

Interferometry based high-precision dilatometry for dimensional characterization of highly stable materials

Meas. Sci. Technol., 20.

[6] Okaji, M., Yamada, N,. Moriyama, H. (2000). Ultra-precise thermal expansion measurements of ceramic

and steel gauge blocks with an interferometric dilatometer. Metrologia, 37, 165−171.

[7] Demtröder, W. (2008). Laser Spectroscopy: Vol. 1: Basic. Principles Springer-Verlag Berlin Heidelberg.

[8] Petru, F., Cip, O. (1999). Problems regarding linearity of data of a laser interferometer with a single

frequency laser. Precis. Eng., 23(1), 39–50.

[9] McMurtry, D. (2002). Interferometer. WO 02/34321 A1.

[10] Patent no PL387343.

[11] Dobosz, M., Zamiela, G. (2012). Interference fringe detection system for distance measuring interferometer.

Optics and Laser Technology, 44, 1620−1628.

[12] Edlén, B. (1966). The refractive index of air. Metrologia, 2, 71−80.

[13] Birch, K.P. Downs, M.J. (1993). An updated Edlén equation for the refractive index of air. Metrologia, 30,

155−162.

[14] Birch, K.P., Downs, M.J. (1994). Correction to the updated Edlén equation for the refractive index of air.

Metrologia, 31, 315−316.


_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Sep. 26, 2016; accepted on Jan. 29, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0034.


Index 330930, ISSN 0860-8229


LEAKAGE CURRENT DEGRADATION DUE TO ION DRIFT AND DIFFUSION IN TANTALUM AND NIOBIUM OXIDE CAPACITORS

Martin Kuparowitz, Vlasta Sedlakova, Lubomir Grmela

Brno University of Technology, Faculty of Electrical Engineering and Communication, Technicka 8, 616 00 Brno, Czech Republic ([email protected], [email protected], +420 541 146 025, [email protected])

Abstract

High temperature and high electric field applications in tantalum and niobium capacitors are limited by the mechanism of ion migration and field crystallization in a tantalum or niobium pentoxide insulating layer.

The study of leakage current (DCL) variation in time as a result of increasing temperature and electric field might

provide information about the physical mechanism of degradation. The experiments were performed on tantalum

and niobium oxide capacitors at temperatures of about 125°C and applied voltages ranging up to rated voltages

of 35 V and 16 V for tantalum and niobium oxide capacitors, respectively. Homogeneous distribution of oxygen

vacancies acting as positive ions within the pentoxide layer was assumed before the experiments. DCL vs. time characteristics at a fixed temperature have several phases. At the beginning of ageing the DCL increases

exponentially with time. In this period ions in the insulating layer are being moved in the electric field by drift

only. Due to that the concentration of ions near the cathode increases producing a positively charged region near

the cathode. The electric field near the cathode increases and the potential barrier between the cathode and

insulating layer decreases which results in increasing DCL. However, redistribution of positive ions in the insulator

layer leads to creation of a ion concentration gradient which results in a gradual increase of the ion diffusion current in the direction opposite to the ion drift current component. The equilibrium between the two for a given

temperature and electric field results in saturation of the leakage current value. DCL vs. time characteristics are

described by the exponential stretched law. We found that during the initial part of ageing an exponent n = 1

applies. That corresponds to the ion drift motion only. After long-time application of the electric field at a high

temperature the DCL vs. time characteristics are described by the exponential stretched law with an exponent

n = 0.5. Here, the equilibrium between the ion drift and diffusion is achieved. The process of leakage current degradation is therefore partially reversible. When the external electric field is lowered, or the samples are

shortened, the leakage current for a given voltage decreases with time and the DCL vs. time characteristics are

described by the exponential stretched law with an exponent n = 0.5, thus the ion redistribution by diffusion

becomes dominant.

Keywords: niobium oxide capacitors, tantalum capacitors, leakage current, ion diffusion, ion drift.


1. Introduction

Quality and life time of capacitor and supercapacitor devices have been studied for the last

decades by many scientists [1−11]. The degradation of tantalum (Ta) and niobium oxide (NbO)

capacitors in steady-state conditions at elevated temperatures was studied in [6−11]. The

capacitor leakage current (DCL) is a parameter most sensitive to defects and irreversible processes in the insulating pentoxide layer. Changes of DCL in time at increased temperature

and applied electric field might provide information on the physical mechanism of degradation. High temperature and high electric field applications are considered to be limited by field

crystallization mechanisms and by migration of positively charged oxygen vacancies (ions)

in pentoxide film [6−9]. The field crystallization model assumes that tantalum or niobium oxide crystals grow with time of operation under the amorphous anodic oxide and eventually disrupt

M. Kuparowitz, V.Sedlakova, L. Grmela: LEAKAGE CURRENT DEGRADATION DUE TO ION DRIFT …

the dielectric layer, causing a breakdown. Until the moment of disruption no changes in leakage

currents are observed. It is assumed that the rate of crystallization increases with increasing thickness of the anodic pentoxide [7] and then high-voltage capacitors should be more vulnerable to this type of failure.

The model of redistribution of positive ions in pentoxide film [7] assumes that ions move from the capacitor anode to its cathode in electric field by diffusion only and create an internal

electric field in the vicinity of insulating layer-cathode interface which affects the potential barrier on this interface according to a modified Schottky conduction mechanism and consequently changes DCL.

Leakage current variations are partially reversible [10−12]. Increasing temperature results in a gradual decrease of leakage currents either without applying an external electric field or with

applying a very low voltage. In some cases initial values of DCL were restored altogether. When the leakage current changes are reversible and the field crystallization is not involved, the source of DCL change must only be the ion redistribution.

Both Ta and NbO capacitors pass through high temperature technological steps which should ensure homogeneous distribution of oxygen vacancies in the dielectric layer. Therefore, we

assume that the concentration of positive ions – oxygen vacancies in the pentoxide volume is constant if the experiments are performed on as-prepared samples (not subjected to an external electric field prior to the experiment). In this case the ion diffusion cannot be involved in the

charge redistribution in the pentoxide volume, because no concentration gradient exists within the pentoxide layer at the beginning of ageing. Drift of charges in the external electric field

must be observed first, whereas diffusion of charges occurs only after the concentration gradient is formed within the structure.

The ageing process in Ta and NbO capacitors can be divided into two separate phases.

During the initial stage of ageing the drift process is dominant due to the application of external electric field at an elevated temperature. The second stage of ageing is affected by both the

external electric field and the ion concentration gradient created in the vicinity of Ta2O5 or Nb2O5 – cathode interface. In this case both drift and diffusion of ions are pronounced.

In this paper we show a method of the qualitative evaluation of ion drift and diffusion

processes during the ageing of Ta and NbO capacitors. Time dependencies of the leakage current are measured and evaluated and mechanisms responsible for the DCL increase are

determined. The reversibility of DCL changes and their source are verified.

2. Experiment

The experiments were performed on tantalum capacitors with capacitance 33 µF and

nominal voltage 35 V and niobium oxide capacitors with capacitance 2.2 µF and nominal voltage 16 V. All capacitors contain an MnO2 cathode and are placed in an SMD type D case

with dimensions 7.3 × 4.3 × 2.9 millimetres (length × width × height). The working temperature

is in a range of −55 to +125°C. The dielectric thickness is about 190 nm for Ta capacitors and 170 nm for NbO capacitors. We have evaluated two sets of Ta capacitors denoted further as Ta1 and LT8, and a set of NbO capacitors denoted as NbO2. 20 samples were evaluated within each set.

We measured the leakage current evolution in time for samples powered at a nominal voltage and placed in a climatic chamber at temperature 120°C for NbO capacitors and 125°C for Ta

capacitors. The leakage currents were monitored using a PC-based data acquisition system (see Fig. 1).

Here, the samples under test were soldered on an FR4 board with printed connectors, which

enables simultaneous charging of up to 20 samples. PCBs with soldered samples were placed in a climatic chamber, where an appropriate value of temperature can be maintained within

256


a range from 30 to 300°C. The samples were connected to load resistors using multiple cables

with temperature-proof PTFE insulation. The 10 kΩ load resistors were placed outside the

climatic chamber. The samples were powered using a DC digital power source Agilent 6614C. To measure the voltage on the load resistors an Agilent 34970A meter with 3 pcs of a 20-channel multiplexer card 34901A was used. The climatic chamber, multi-meter and power

source were interconnected via an IEEE 488 (GPIB) bus which was connected to the computer via a GPIB/USB interface Agilent 82357A.

Fig. 1. A measurement system.

For measurement of the leakage current time dependence at an elevated temperature

a required voltage of the power source was fixed. A voltage on the load resistor was measured periodically every 10 seconds. The leakage current value was calculated from the voltage measured on the load resistor and the load resistor value. The values of load resistors should

meet the condition that the voltage on the load resistor during the experiment does not exceed 5% of the power source output voltage. Then the voltage on the measured capacitor was

assumed to be constant during the experiment. The total duration of ageing experiment was near 400 hours.

Fig. 2. A DCL vs. time characteristic for the niobium oxide capacitor NbO2-3 ageing at a nominal voltage

V = 16 V and temperature T = 120°C.

A typical dependence measured during the experiment is shown in Fig. 2. Here, the time

dependence of leakage current is shown for the niobium oxide capacitor NbO2-3 for applied

nominal voltage V = 16 V at temperature T = 120°C. The monitored leakage current value

increases from 19 µA up to 88 µA within a time interval of 400 hours (see Fig. 2).

0

20

40

60

80

100

00.4x10

60.8x10

61.2x10

61.6x10

6

0 1x102

2x102

3x102

4x102

t / h

Nb02-3T = 120 °CU = 16 V1TT

I=a+c(1-exp(-(t/b)n))

a=19, b=1.97E5, c=71.9, n=0.572

t / s

I / µ

A

257


After this the leakage current recovery was studied. The voltage was lowered down to 5 V

for Ta capacitors and to 2 V for NbO capacitors. The leakage current was then monitored in about 40 to 170 hours.

Figure 3 shows DCL recovery for the niobium oxide capacitor NbO2-3. After long-time

application of a nominal voltage at 120°C (see Fig. 2) the voltage was lowered to 2 V and the

sample was left at 120°C. The monitored leakage current value decreased from 1.8 µA to 0.2 µA

within a time interval of about 40 hours. A drop of current from 88 µA to 1.8 µA is caused by a decrease of the applied voltage from 16 V to 2 V.

Fig. 3. A DCL vs. time characteristic for the niobium oxide capacitor NbO2-3 during leakage current recovery

for applied voltage V = 2 V at temperature T = 120°C.

3. Results and discussion

The effect of electric field and high temperature on the ion drift and diffusion in tantalum

and niobium oxide capacitors will be discussed. We suppose that oxygen vacancies in a tantalum or niobium pentoxide layer act as positive ions. The samples are, as produced, stored at a room temperature without application of voltage before this experiment. Therefore, we

suppose that oxygen vacancies in the insulating layer are homogeneously distributed according to the thermodynamic equilibrium. This ion distribution is altered by applying an electric field.

The concentration of positive ions near cathode increases due to the ion drift in the electric field. The increase of concentration of positive ions in the vicinity of insulator/cathode interface results in an exponential increase of the leakage current.

Redistribution of positive ions in the insulator volume leads to the creation of an ion concentration gradient which results in a gradual increase of the ion diffusion current in the

direction opposite to that of the ion drift current component. The equilibrium between the ion drift in the electric field (from anode to cathode) and the ion diffusion due to the formed concentration gradient (in the direction from cathode to anode) for a given temperature and

electric field results in saturation of the leakage current value. The leakage current time dependence during ageing of a capacitor is described by an

exponential function:

)))/(exp(1()(10

n

tIItI τ−−+= , (1)

where: I0 is a DCL value at the beginning of ageing; I1 is a change of DCL due to the ageing, τ is a time constant of the ageing process. The value of exponent n = 1 when the potential barrier

0

0.5

1.0

1.5

2.0

00.5x10

51.0x10

51.5x10

5

0 10 20 30 40 t/h

y=a+cexp(-(x/b)n)

a=0.202, b=6076, c=1.60, n=0.5

Nb02-3T = 120 °CV = 2 V

t / s

I / µA

258


on the insulating layer/cathode interface linearly decreases due to the ion drift in the electric

field [13]. The value of exponent n = 0.5 is only for the ion diffusion [6, 7].

3.1. Effect of ion drift on leakage current at beginning of ageing

DCL vs. time characteristics for initial 1 to 10 hours of ageing of tantalum capacitors

at a rated voltage 35 V and temperature 125°C and niobium oxide capacitors at a rated voltage 16 V and temperature 120°C are shown in Figs. 4 and 5, respectively.

Fig. 4. DCL vs. time characteristics for a nominal voltage V = 35 V at temperature T = 125°C − beginning

of the ageing process for the tantalum capacitor Ta1-6.

Fig. 5. DCL vs. time characteristics for a nominal voltage V = 16 V at temperature T = 120°C − beginning

of the ageing process for the niobium oxide capacitor NbO2-3.

At the beginning of ageing the electron transport is mostly controlled by the ion drift from

anode to cathode. The measured time dependencies of leakage current can be modelled by (1)

using an exponent n = 1 during the first 1 hour for a tantalum capacitor and during the first 10 hours for a niobium oxide capacitor. A starting value of DCL at the beginning of ageing is

9

10

11

12

13

01x10

32x10

33x10

34x10

35x10

3

0 0.2 0.4 0.6 0.8 1.0 1.2

6

I=a+c(1-exp(-t/b))

a=10, b=2979, c=3.29

t / h

Ta1-6

T = 125 °C

V = 35 V

t / s

I / µA

20

30

40

01x10

42x10

43x10

44x10

4

0 2 4 6 8 10

3

I=a+c(1-exp(-t/b))

a=18.6, b=3.79E4, c=34.5

t / h

Nb02-3

T = 120 °CV = 16 V

t / s

I / µA

259


I(0) = 10 µA for sample Ta1-6 and I(0) = 18.9 µA for sample Nb02-3. A time constant of ageing process determined from the fit of experimental data is about 3000 s for sample Ta1-6 and about

3.8 × 104 s for sample NbO2-3 considering the ion redistribution caused only by drift in the

electric field. A time constant for niobium oxide capacitors is higher due to a lower applied electric field and a slightly lower temperature during the ageing process.

3.2. Effect of medium-term application of electric field on ion transport in insulating layer

A time dependence of the leakage current of tantalum sample Ta1-4 within the initial 5 hours

of ageing is shown in Fig. 6. Here, the experimental data are modelled by (1) using the exponent

value n = 0.629.

Fig. 6. DCL vs. time characteristics for the tantalum capacitor Ta1-4 for a nominal voltage V = 35 V

at temperature T = 125°C – initial 5 hours of the ageing process. A model of experimental data includes

the ion movement by both drift and diffusion.

The exponent n values in a range from 0.5 to 1 correspond to the ion movement by both drift

and diffusion. The drift transport from anode to cathode is a result of the external electric field.

The ion diffusion in the opposite direction appears as a result of the ion concentration gradient formed in the vicinity of cathode interface. However, during medium-term application of the

electric field the drift transport mechanism still remains dominant. During long-term application of the electric field the equilibrium of the ionic drift and the

diffusion transport mechanism is achieved.

3.3. Effect of long-term application of electric field on ion transport in insulating layer

A DCL vs. time characteristic for tantalum capacitor Ta1-4 when a voltage V = 35 V

at temperature 125°C was applied within a time interval of 80 hours is shown in Fig. 7. Fig. 2 shows the time dependence of leakage current for niobium oxide capacitor NbO2-3 for an applied nominal voltage V = 16 V at temperature T = 120°C in a time interval of 400 hours.

In both cases the measured time dependencies of leakage current can be modelled by (1)

with an exponent n ≈ 0.5. A starting value of DCL at the beginning of ageing is I(0) = 10 µA

for sample Ta1-4 and I(0) = 19 µA for sample Nb02-3. A time constant of the ageing process

is τ = 2.10 × 104 s for sample Ta1-4 and τ = 1.97x105

s for sample NbO2-3 considering the ion redistribution by both drift in electric field and the diffusion mechanism. A time constant for

0

20

40

60

00.5x10

41.0x10

41.5x10

42.0x10

4

0 1 2 3 4 5

4

t / h

Ta1-4T = 125 °CV = 35 V


a=10, b=5922, c=47.6, n=0.629

t / s

I / µA

260


niobium oxide capacitors is about one order of magnitude higher due to a lower applied electric

field and a slightly lower temperature during ageing.

The monitored leakage current value increases from 10 µA to 73 µA within a time interval

of 80 hours for sample Ta1-4, while the expected DCL value at saturation is 74.46 µA. The

monitored leakage current value increases from 19 µA to 88 µA within a time interval of 400

hours for sample NbO2-3, while the expected DCL value at saturation is 90.9 µA.

Fig. 7. DCL vs. time characteristics for the tantalum capacitor Ta1-4 for a nominal voltage

V = 35 V at temperature T = 125°C.

3.4. Reversibility of leakage current changes

When the external electric field is lowered or switched off, the ion drift component decreases or drops down to zero. The concentration of positive ions in the vicinity of insulating layer/cathode interface is higher compared with its value in the insulating layer volume. The

diffusion of ions due to the concentration gradient becomes the dominant ion transport mechanism in the tantalum or niobium pentoxide layer. The ions – oxygen vacancies – diffuse

in the direction from cathode to anode to restore the homogeneous distribution of ions in the pentoxide layer volume. A decrease of the positive ion concentration, in the vicinity of insulating layer/cathode interface, results in an increase of the corresponding potential barrier

and consequently in a decrease of the capacitor’s leakage current. A leakage current vs. time dependence during the recovery process is described by:

))/(exp()(10

n

tIItI τ−+= , (2)

where: I0 is an expected value of the leakage current for the time at infinity; I1 is a value of the

leakage current lowering due to the ion redistribution in the pentoxide layer and τ is a time

constant of the recovery process. The exponent is n ≈ 0.5 for both short-time and long-time

periods. It means that the ion diffusion is the dominant transport mechanism within the recovery process.

Figure 3 shows DCL recovery after long-time application of a nominal voltage V = 16 V at 120°C. Here, a time dependence of the leakage current is shown for niobium oxide capacitor NbO2-3 for a voltage lowered down to V = 2 V at temperature T = 120°C. The monitored

leakage current value decreases from 1.8 µA to 0.2 µA within a time interval of about 40 hours. A time constant of the recovery process for niobium oxide sample NbO2-3 is about 6000

0

20

40

60

80

01x10

52x10

53x10

5

0 20 40 60 80

10

4

t / h

Ta1-4T = 125 °CV = 35 V


a=10, b=2.10E4, c=64.46, n=0.5

t / s

I / µA

261


seconds. We can see that an equilibrium value I0 = 0.20 µA is achieved within the monitored time interval.

Fig. 8. DCL vs. time characteristics for the tantalum capacitor LT8-1 with an applied voltage

V = 5 V at temperature T = 125°C during a leakage current recovery.

A similar experiment was performed on the tantalum capacitor LT8-1. A DCL recovery after

long-time application of a nominal voltage V = 35 V at 125°C is shown in Fig. 8. Here, a time dependence of the leakage current is shown for a voltage lowered down to V = 5 V at

temperature T = 125°C. The monitored leakage current value decreases from 2.3 µA to 0.1 µA within a time interval of about 170 hours. A time constant of the recovery process for tantalum

sample LT8-1 is 3.25 × 104 seconds. We can see that an equilibrium value I0 = 0.076 µA is not achieved within the monitored time interval. The higher time constant determined for the

tantalum sample is probably affected by a higher external electric field acting on the sample during the recovery experiment.

4. Conclusions

A method for the qualitative evaluation of ion drift and diffusion processes during ageing of Ta and NbO capacitors at an elevated temperature is presented. Time dependencies of DCL are measured for a rated voltage at temperature 125°C for Ta capacitors and 120°C for NbO

capacitors. The mechanisms responsible for a DCL increase are determined using the parameters of exponential fit of the measured data.

Oxygen vacancies in a tantalum and niobium pentoxide layer act as positive ions. The homogenous distribution of ions corresponding to the thermodynamic equilibrium is supposed to have occurred before ageing. After application of an electric field the ion distribution is

changed due to ability of the ions to move. The concentration of positive ions near cathode increases due to the ion drift in the electric field. An increase of the positive ion concentration

in the vicinity of insulator/cathode interface results in an exponential increase of the leakage current. A time constant of the ageing process due to the ion drift decreases with increasing the

electric field and an exponent n = 1 for a linear decrease of the potential barrier on the insulating layer/cathode interface due to the ion drift in the electric field only.

Redistribution of positive ions in the insulator volume leads to creation of an ion

concentration gradient, which results in a gradual increase of the ion diffusion current in the

0

0.5

1.0

1.5

2.0

2.5

02x10

54x10

56x10

5

0 50 100 150 t / h

LT8-1

T = 125 °CV = 5 VRecovery

I=a+cexp(-(t/b)n)

a=0.0761, b=3.25E4, c=2.22, n=0.5

t / s

I / µA

262


direction opposite to that of the ion drift current component. The equilibrium between the two,

for a given temperature and electric field, results in saturation of the leakage current value. The exponent n value decreases with an increase of value ion diffusion current from 1 to 0.5, whereas n = 0.5 when the equilibrium between the ion drift and diffusion is achieved.

DCL changes are fully reversible when the source of DCL increase is only the ion redistribution by drift and diffusion. The samples left at an elevated temperature react to an

external electric field drop with a progressive decrease of DCL in time. From the exponential

fit of measured DCL time dependence we derived the exponent value n ≈ 0.5 for both short-

time and long-time periods. It means that the ion diffusion is the dominant transport mechanism

within the DCL recovery process. A time constant of the recovery process is directly proportional to the external electric field value.

Acknowledgements

Research described in this paper was financed by Czech Ministry of Education in the frame of National Sustainability Program under grant LO1401. For research, the infrastructure of the SIX Center was used.

References

[1] Sedlakova, V., Sikula, J., Majzner, J., Sedlak, P., Kuparowitz, T., Buergler, B., Vasina, P. (2016).

Supercapacitor Degradation Assesment by Power Cycling and Calendar Life Tests. Metrol. Meas. Syst.,

23(3), 345−358.

[2] Szewczyk, A., Sikula, J., Sedlakova, V., Majzner, J., Sedlak, P., Kuparowitz, T. (2016). Voltage Dependence

of Supercapacitor Capacitance. Metrol. Meas. Syst., 23(3), 403−411.

[3] Smulko, J., Józwiak, K., Olesz, M., Hasse, L. (2011). Acoustic emission for detecting deterioration

of capacitors under aging. Microelectronics Reliability, 51(3), 621−627.

[4] Smulko, J., Józwiak, K., Olesz, M. (2012). Quality testing methods of foil-based capacitors. Microelectronics

Reliability, 52(3), 603−609.

[5] Pavelka, J., Sikula, J., Vasina, P., Sedlakova, V., Tacano, M., Hashiguchi, S. (2002). Noise and transport

characterisation of tantalum capacitors. Microelectronics Reliability, 42, 841−847.

[6] Teverovsky, A. (2010). Effect of Post-HALT Annealing on Leakage Currents in Solid Tantalum Capacitors,

CARTS USA 2010, 43–59.

[7] Teverovsky, A. (2010). Degradation of leakage currents in solid tantalum capacitors under steady-state bias

conditions. Electronic Components and Technology Conference (ECTC). Proc. 60th, 2010, 752−757.

[8] Zednicek, T., Sikula, J., Leibovitz, H. (2009). A Study of Field Crystallization in Tantalum Capacitors and

its effect on DCL and Reliability. 29th CARTS 2009, Jacksonville, FL, 5.3.1–11.

[9] Sikula, J., Sedlakova, V., Navarova, H., Hlavka, J., Tacano, M., Zednicek, T. (2008). Tantalum and Niobium

Oxide High Voltage Capacitors: Field Crystallization and Leakage Current Kinetics. CARTS Europe 2008,

Helsinki, Finland, Oct. 20–23, 2008, 267–276.

[10] Laleko, V.A., Odinets, L.L., Stefanovich, G.B. (1982) Ionic current and kinetics of activation of the

conductivity of anodic oxide films on tantalum in strong electric fields. Soviet Electrochemistry, 18,

743−746.

[11] Chaneliere, C., et al. (1998). Tantalum pentoxide (Ta2O5) thin films for advanced dielectric applications.

Material Science and Eng., R22, 269−322.

[12] Sikula, J., Sedlakova, V., Navarova, H., Kopecky, M., Zednicek, T. (2011). Ion Diffusion and Field

Crystallization in Niobium Oxide Capacitors. CARTS Europe 2011, Nice, France, 33–41.

263


[13] Elhadidy, H., Grill, R., Franc, J., Sik, O., Moravec, P., Schneeweiss, O. (2015). Ion electromigration in CdTe

Schottky metal-semiconductor-metal structure. Solid State Ionics, 278, 20−25.


_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Jun. 30, 2016; accepted on Oct. 22, 2016; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0021.


Index 330930, ISSN 0860-8229


SEQUENTIAL CLASSIFICATION OF PALM GESTURES BASED

ON A* ALGORITHM AND MLP NEURAL NETWORK FOR QUADROCOPTER

CONTROL

Marek Wodziński, Aleksandra Krzyżanowska

AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics Computer Science and Biomedical Engineering, A. Mickiewicza 30, 30-059 Cracow, Poland ( [email protected], + 48 12 617 2222 , [email protected])

Abstract

This paper presents an alternative approach to the sequential data classification, based on traditional machine

learning algorithms (neural networks, principal component analysis, multivariate Gaussian anomaly detector) and

finding the shortest path in a directed acyclic graph, using A* algorithm with a regression-based heuristic. Palm

gestures were used as an example of the sequential data and a quadrocopter was the controlled object. The study

includes creation of a conceptual model and practical construction of a system using the GPU to ensure the real-

time operation. The results present the classification accuracy of chosen gestures and comparison of the

computation time between the CPU- and GPU-based solutions.

Keywords: machine learning, shortest path, sequential data, quadrocopter, GPU, CUDA.


1. Introduction

Object control using biomedical signals, which are an example of the sequential data, is an important area of current research because a lot of disabled persons need an alternative way

to interact with their surroundings. So far, many attempts were made to control various systems and devices, using biomedical signals. For example, partially paralyzed people can still use EEG [1], EMG [2], EOG [3] signals, as an HMI interface to perform basic actions, or visually impaired people can interact with a computer using palm gestures [4].

Most common difficulties arising during such projects include the requirement of real-time

control and generalization due to inter-individual variation [1−6]. A typical approach to the

problem of generalization is the machine learning technique. The stronger the requirement of generalization, the more training data is required, which implies a higher model complexity

and a greater computational cost [7]. The real-time implementation of machine learning algorithms is difficult when the model has a high complexity [7]. Therefore, parallel

implementations based on GPU and FPGA have been developed [8−10]. However, GPU parallelization of the sequential data classification using, for example, Hidden Markov Models [11], is not easy and varies strongly with the data type [12]. Moreover, the implementation

process is quite difficult and requires the programming expertise. We suggest an alternative approach to the problem of sequential data classification, which

involves separation of a single classification frame from the result conjunction by using

traditional machine learning algorithms and finding the shortest path in a directed acyclic graph to determine the most probable outcome. Such a solution enables highly parallelizable

implementation and effective use of GPU. We decided to use a quadrocopter as the controlled object. Regarding its high complexity and six degrees of freedom, it is important to design a precise and reliable control scheme. The palm movements were registered using a Leap Motion

M. Wodziński, A. Krzyżanowska: SEQUENTIAL CLASSIFICATION OF PALM GESTURES BASED …

sensor which is described in detail in Subsection 2.2. We primarily focus on the requirement

of real-time system operation. To our knowledge, this is the first work that shows how to bring down classification of the sequential data to the problem of finding the shortest path.

2. Suggested solution

2.1. Solution concept

A conceptual model was divided into several parts, including: registration of palm

movements, creation of a palm model, feature extraction, anomaly detection, gesture classification, an update of the graph structure, solving the shortest path problem using A*

algorithm, mapping of the results, creation and transmission of commands − as shown in

a processing graph in Fig. 1.

Fig. 1. A scheme of acquisition, processing, classification and control.

Palm

movements

registration

Palm model

creation

Features

extraction

Gestures

classification

Anomaly

detection

Graph

structure

update

Finding

shortest path

with A*

algorithm

Classification

results

mapping

Command

transmission to

quadrocopter

Training

Data

CPU

GPU

Legend:

Signal

Command

266


2.2. Data acquisition and feature extraction

For registration of palm movements, a Leap Motion (Fig. 2a) sensor was used, which

measures various parameters of palm and fingers, including their position, velocity, direction and geometry (Fig. 2b), using monochromatic infrared cameras and LEDs [13]. The operation

range varies from 25 to 650 millimetres above the controller. The average accuracy of the sensor is about 0.7 millimetres [14]. The Leap Motion controller does not perform any computations, therefore the acquisition and processing speed depend strongly on the used PC specification.

The details of Leap Motion hardware specification and software operations were not disclosed by the manufacturer. The Leap Motion sensor software is able to recognize palm gestures by

itself, without using external algorithms. The recognized gestures include circle, swipe, key tap, and screen tap [15]. However, due to the lack of customization capability and a relatively high computational cost, we decided to not use this feature and the customized recognition

algorithms were implemented. Each frame of raw data contained 104 features (36 positions, 36 velocities, 12 directions, 10 finger widths, 10 finger lengths). The acquisition frequency

depended on the used hardware and varied from 90 Hz to 180 Hz. a) b)

Fig. 2. A photo of a Leap Motion sensor and visualization of a palm.

Leap Motion Controller (a); palm skeleton frame (b).

The raw data acquired using the Leap Motion sensor were not enough to accurately classify

gestures, so a palm model including additional information was built. We added extra categorical variables mapping fingers to their types and determining which hand is left, and

which is right. In addition, we normalized the palm size. All calculations used to create the palm model were based on the position, direction, and geometry data. If the model could not be created, e.g. because one hand had been unavailable, the data frame was rejected. The output

frame contained 160 features. To reduce the frame size, the principal component analysis (PCA) was used, based on the

singular decomposition of a covariance matrix (1−2) [7].

∑

, (1)

, (2)

where denotes a covariance matrix; denotes the n-th feature vector; diagonal entries of

are the singular values of , and columns of and are left-singular vectors and right-singular

vectors of , respectively. We retained 99% of data variance (3), which decreased the frame size to 124 features.

∑

∑

0.99, (3)

where K denotes the size of output data.

267


A summary of the data processing performed in this paragraph is shown in Fig. 3.

Fig. 3. A summary of the data processing performed in Paragraph 2.2.

2.3. Single frame classification

The purpose of next step was to perform fast detection of invalid gestures. To achieve this, we decided to use a multivariate Gaussian anomaly detector (4) [7]. Another possibility was to

use a standard Gaussian anomaly detector, which was computationally cheaper, but greatly increased the problem complexity due to the requirement of manual creation of correlated

features.

| , =

||

−

− − , (4)

where denotes the anomaly feature vector and D is a dimension of the vector .

Since the goal was to perform fast anomaly detection, we could not use all features used in further classification. Therefore, a small subset of features was chosen and separate training

data were created, based on experimental results. We chose a subset of finger positions and directions from the training data and created additional data not related to any desired gesture,

which denoted an anomaly. In general, 95% of training data were considered as a normal entry, and 5% as an anomaly. If an anomaly was detected, the data frame was rejected.

To classify a gesture frame we used a single-direction multilayer perceptron (MLP) −

regularized artificial neural network with sigmoid neurons (with a cost function as shown in (5) [7]) trained with a backpropagation algorithm, because of its highly parallelizable structure and ease of implementation.

= −

∑ ∑

ℎ

+ 1 − 1 − ℎ

+

∑ ∑ ∑

()

, (5)

where is the reduced size feature vector after applying PCA; denotes a cost function; is

the matrix of network parameters; ℎ is a sigmoid function; is a desired classification output;

denotes a regularization coefficient; M is the input data size; K denotes the number of classes

and L − the number of layers. A summary of the data processing performed in this paragraph is shown in Fig. 4.

Palm

movements

registration

Palm model

creation

Features

extraction

Raw data (104

features per

frame)

Additional

features (160

features per

frame)

PCA reduces

frame size

(124 features

per frame)

268



Fig. 5. Visualisation of the classified gestures.

269


The gestures (as shown by visualization of gestures in Fig. 5) were classified as follows:

1. take off (the left palm assemble); 2. landing (the right palm assemble); 3. position maintenance (keeping palms horizontally);

4. taking a snapshot (fast both hands’ assemble); 5. magnetometer calibration (circles with both hands simultaneously in the same direction);

6. falloff simulation (circles with both hands simultaneously in opposite directions); 7. flip right (a circle with the right hand to the right); 8. flip left (a circle with the right hand to the left);

9. flip forward (a circle with the right hand forward); 10. flip backward (a circle with the right hand backward);

11. yaw control (changing the yaw angle of the left hand); 12. emergency call (slow both hands’ assemble); 13. roll/pitch control (changing the pitch angle of the left hand);

14. vertical speed control (changing the pitch of the right hand); 15. both roll/pitch and vertical control (changing the pitch and roll of the right hand),

which resulted in the output layer containing 15 neurons.

2.4. Sequential data classification

The classification process described in Subsection 2.3 takes into account only single frames.

However, a palm gesture is an example of sequential data, which spreads over time. Therefore, an appropriate structure needs to maintain the relation between classification frames. The chosen structure was a directed acyclic graph (DAG), as shown in Fig. 6, with a virtual root

(VR), where each level represents a single classification frame, each vertex represents a single classification possibility and each edge contains a normalized inverse probability of transition

to a particular vertex, calculated by MLP. The graph was not created in each iteration but circularly updated with a predefined buffer size (i.e. one calculated to accommodate around 2

seconds of input data) based on the array implementation, which greatly improved the execution time in comparison with the list or object relation. Each successful classification replaced one row in the array and pointed VR output edges to the oldest maintained frame.

Fig. 6. A DAG structure used to classify the sequential data.

In the next step the shortest path in DAG was searched with A* algorithm. This process enabled to find the most probable gesture based on the preceding observations. The heuristic

V11 V12 V13 V1N...

V21 V22 V23 V2N...

VM1 VM2 VM3 VMN...VM1

Classification

Frame

---------------------------------------------------------------------------------------------------------------------------------

VR

270


calculation was done by linear regression with separate training data. The input of the regression

function was the classification result from the MLP. It is important to notice that each iteration updated only a single row, so the results from the preceding algorithm run were placed on a stack to accelerate the next iteration. In addition, the traditional priority queue implementation

was expanded to take advantage of the preceding results’ stack. We applied the found shortest path to determine the next action with a recursive procedure checking which classification

output in the sequence was the most frequently visited. In the last step the classification results were translated to a command transmitted to the

quadrocopter. We used a Parrot AR Drone 2.0 communicating with a PC using TCP and UDP

protocols. We built the communication libraries based on a vanilla AR Drone firmware [16]. We chose this concrete drone due to easier communication with it, in comparison with RC

models. A summary of the data processing performed in this paragraph is shown in Fig. 7.


3. Parallel GPU-based implementation

It is important to notice that the conceptual model would not be effective without optimized,

paralleled and pipelined implementation of it because the real-time operation requirement

would not be met. We developed a special software architecture to manage the GPU resources, training data, and graph structure, as shown in Fig. 8. The most important technology we used

was Computed Unified Device Architecture (CUDA), which is dedicated to managing multi-core processors, especially GPUs. The software was created in LabVIEW, Python, C# and C++ programming languages.

We parallelized threads performing most of the matrix-based calculation using the CUDA technology. It enabled to greatly improve the computation speed (see Section 4.) and to make

the conceptual model useful in practice, even with a relatively low-cost hardware. We pipelined each step, where rejection of a data frame could occur by using event-based priority queues, with a priority calculated by the resource manager thread. We applied the pipelining technique

because ML steps could reject an inappropriate data frame, which with its monolithic architecture would lead to a system instability.

271


We separated the teaching process from the usage of trained models. Such a separation

enabled to implement a manual, adaptive learning scheme without interrupting the system operation. All model learning parameters were stored in XML and binary files. The binary files were streamed to GPU memory in regular time intervals, while the XML files were used in the

prototype solution.

Fig. 8. Implementation of machine learning blocks based on the CUDA technology.

The graph computations were performed by the CPU due to the sequential nature and relatively low usage of resources. We applied a separate data set to compute the heuristic

function and threshold its output to ensure admissibility and consistency. In practice, it decreased the classification accuracy (by 2.3% on average), but guaranteed derivation of the

shortest path. 4. Results

The GPU-based implementation increased the conceptual model frequency (the number

of commands send to the quadrocopter, based on palm movements, per second) around 10 times in comparison with the pure CPU implementation, as shown in Fig. 6. The implementation based only on CPU could not be used in practice due to noticeable delays in the quadrocopter

control, which made users unable to synchronize hand movements. The computations performed by GPU made the control smooth, even with a relatively low-cost hardware. Fig. 9

CUDA Resource

Pool Manager

A* Graph Solver

with regression

based heuristic

Pipe I

CUDA

Thread I

CUDA

Thread II

CUDA

Thread III

CUDA

Thread N

...

Features

extraction

CUDA

Thread I

CUDA

Thread II

CUDA

Thread III

CUDA

Thread N

...

Anomaly

detection

Pipe II

CUDA

Thread I

CUDA

Thread II

CUDA

Thread III

CUDA

Thread N

...

Gestures

classification

Pipe III

Anomaly

Data

Classification

Data

Heuristic

Data

Training Data

Learning

Structures

Trainer

CPU

GPU

Legend:

272


shows also that A* algorithm is not in the hot path since in both solutions it was implemented

on CPU. The accuracy of gesture detection varied strongly on the gesture type and the environmental

conditions (as the accuracy we define a ratio of valid/invalid commands sent to the quadrocopter

when a given action was requested). The averaged accuracies are shown in Table 1.

Fig. 9. Comparison of the computing frequency between CPU- and GPU-based solutions.

Table 1. Comparison of the palm gesture detection accuracy in different environmental conditions.

Gesture type Acc. inside building [%] Acc. low insolation [%] Acc. high insolation [%]

Takeoff 100.00 96.27 81.78

Landing 100.00 97.09 77.47

Position maintenance 100.00 100.00 97.82

Taking snapshot 91.34 81.98 62.62

Mag. calibration 87.45 83.51 64.05

Falloff simulation 88.52 84.22 65.17

Flip right 95.91 93.23 72.48

Flip left 95.42 93.38 75.81

Flip forward 84.51 81.03 64.40

Flip backward 85.68 79.13 65.91

Yaw control 98.02 95.39 79.08

Vertical speed control 96.33 94.63 77.37

Emergency call 88.79 80.73 59.93

Roll/pitch control 97.93 95.44 77.78

Roll/pitch/vertical control 97.40 95.69 75.49

Even though the data set included 15 complex gestures, a high recognition efficiency was

obtained, especially for gestures based on slow angle changes and single hand assembling. However, it was observed that too high insolation may decrease the detection efficiency because the input data become corrupted. In addition, a strong wind makes control with palm

movements much harder than with a dedicated controller, because the visual feedback is not enough to sense an additional resistance. To address the insolation issue, it is possible either to

use a different signal acquisition hardware or to expand the training data and increase the model complexity.

Moreover, the classification of four gestures (circle, swipe, screen tap and key tap) using the

proposed algorithm was compared with the built-in Leap Motion classification algorithms.

273


The accuracy comparison is shown in Table 2, whereas the performance comparison is

shown in Fig. 10.

Table 2. Comparison of the palm gesture detection accuracy between the suggested solution

and the classification algorithms with built-in Leap Motion.

Gesture type Suggested solution accuracy [%] Leap Motion accuracy [%]

Circle 100.00 100.00

Swipe 97.36 87.27

Screen Tap 94.18 68.30

Key Tap 95.66 65.49

Fig. 10. Comparison of the computing performance between the algorithms with built-in Leap Motion

and the suggested solution.

The suggested solution is faster and more accurate. However, the algorithms with built-in

Leap Motion do not seem to use the GPU and the CPU usage is quite low. Therefore, for applications which do not have a strong real-time requirement and do not require classification

of complex feature sequences but need the hardware resources for other tasks, it may be advisable to use the software provided by the device manufacturer.

In addition, comparison with other papers was made, as shown in Table 3. Since all the

gesture sets were different, an averaged classification accuracy is presented. Moreover, other papers does not include information about the environmental conditions, so we decided to

compare the accuracy in in-door conditions.

Table 3. Comparison of accuracies obtained with methods presented in other papers.

Method Number of gestures Averaged accuracy [%] Accuracy standard deviation [%]

Suggested solution 15 93.82 5.53

SVM [17] 10 91.38 5.96

Naive Bayesian [18] 4 95.00 1.93

FFNN [18] 4 86.67 22.28

DA+HMM [19] 8 98.96 1.22

SVM+HMM [19] 8 98.56 1.01

DA+CRF [19] 8 99.42 0.83

SVM+CRF [19] 8 98.74 0.76

DA [19] 8 87.67 4.97

SVM [19] 8 88.44 4.53

HMM [20] 5 93.08 6.43

274


The table does not contain the most important aspect, i.e. comparison of the computation

efficiency, because the necessary information is not provided in other publications. The available and comparable papers do not present quantitative performance results. One of the papers ([19]) classifies only gestures made with a single palm, which is a relatively easier task.

The results presented in Table 3 show that the solution presented in the paper achieved a high average accuracy for the larger set of classified gestures in comparison with other solutions.

Moreover, it was proved that the classification algorithm speed is high enough to achieve the

real-time control, which is not confirmed for other solutions presented in the literature [17−20].

5. Conclusion and future work

The suggested solution enables the real-time quadrocopter control using palm gestures

recognized by machine learning algorithms. The new approach involves the sequential data classification with separation of the frame classification from the result conjunction, which

enables an easy parallel implementation. The system meets the requirement of gesture recognition in real-time using the approach of searching the shortest path. However, more research is planned to address the issue of environmental conditions.

In the future, it is possible to replace A* algorithm by exploring the DAG properties, which may lead to a more efficient implementation (like that with the Seam Carving technique [21]).

Moreover, we consider using the Kohonen NN to perform automatic adaptive learning [22] during the system operation, instead of the presented manual teaching.

Further optimization of the computation speed is possible by applying FPGA instead of GPU

[8−10, 23−24]. With the FPGA it would be possible to obtain the real-time operation with more sophisticated models containing more training data, resulting in a better classification accuracy. On the other hand, this would also lead to an increase of the hardware cost and system

complexity.

References

[1] Diwakar, S., Bodda, S., Nutakki, C., Nair B.G. (2014). Neural Control using EEG as a BCI Technique for

Low Cost Prosthetic Arms. Conference: Proc. of the International Conference on Neural Computation

Theory and Applications (NCTA-2014).

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Jul. 27, 2016; accepted on Oct. 22, 2016; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0020.


Index 330930, ISSN 0860-8229 www.metrology.pg.gda.pl

VERIFICATION OF A NOVEL METHOD OF DETECTING FAULTS IN MEDIUM-VOLTAGE SYSTEMS WITH COVERED CONDUCTORS

Stanislav Mišák1), Štefan Hamacek1), Mikołaj Bartłomiejczyk2) 1) VŠB-Technical University of Ostrava, Faculty of Safety, Engineering, 17 Listopadu 15/2172, 708 33 Ostrava-Poruba, Czech Republic ([email protected], [email protected]) 2) Gdańsk University of Technology, Faculty of Electrical and Control Engineering, G. Narutowicza 11/12, 80-233 Gdańsk, Poland ( [email protected], +48 58 347 1416)

Abstract

This paper describes the use of new methods of detecting faults in medium-voltage overhead lines built of covered

conductors. The methods mainly address such faults as falling of a conductor, contacting a conductor with a tree

branch, or falling a tree branch across three phases of a medium-voltage conductor. These faults cannot be detected

by current digital relay protection systems. Therefore, a new system that can detect the above mentioned faults

was developed. After having tested its operation, the system has already been implemented to protect medium-

voltage overhead lines built of covered conductors.

Keywords: fault trees, partial discharges, fault diagnosis, power engineering, power overhead lines.


1. Introduction

In today’s technologically developed times, great emphasis is put on providing a reliable supply of electrical energy to households and the transport, industrial and other sectors. New,

advanced technologies and methods of timely fault detection help to faster remove of faults, thus increasing reliability of the electrical energy supplies. A new system of overhead lines with

SAX-type covered conductors (hereinafter CCs) was developed in Finland in 1976 [1−3].

Such overhead lines were built in Norway and Sweden as well, and gradually appeared in other member states of the European Union. Employing CCs in the construction of these overhead lines is not much different from using bare wires in outdoor overhead lines; the only

difference is in using XLPE insulation in the former [4−6]. By using the insulation, a fault rate of these overhead lines is reduced and it is possible to build the lines in places that are not easily

accessible, e.g. in densely forested areas. Unlike typical outdoor overhead lines with AlFe conductors, when a tree branch falls on overhead lines with CCs, an immediate interphase short-circuit does not occur; therefore, the risk of disconnection from the electrical energy supply

is reduced [7, 8]. A disadvantage of operating overhead lines with CCs is the inability to detect a fault, e.g.

in the case of falling of a conductor [9]. When this kind of fault occurs, there is no earth fault and the limit values of digital relay protection starting elements are not exceeded [10, 11]. Hence, digital relay protection systems are not able to detect this type of fault. For such faults,

as well as other types of faults associated with CCs, such as a tree branch falling on or merely

contacting with a CC, partial discharges (hereinafter PDs) – inner, outer and surface PDs − appear in the fault location (e.g. the point of contact between a conductor and the ground or between a tree branch and CC) [12]. These PDs gradually damage the insulation of the lines. The activity of PDs enlarges the area of a fault, and other insulated areas are being degraded.

S. Mišák, Š. Hamacek, M. Bartłomiejczyk: VERIFICATION OF A NOVEL METHOD OF DETECTING …

During this process, the conductor insulation breaks down and causes a fault (interphase or earth fault). The VŠB-TUO team developed a methodology based on the principle of finding a relation between the occurrence and characteristics of PDs and the origin of faults in overhead lines with CCs. Based on this methodology, a number of measurements were made. Using these measurements, procedures for detecting fault indicators in real medium-voltage overhead lines with CCs were gradually created. The effects of PDs can be worsened by other factors, such as humidity, temperature, solar radiation, atmospheric pressure, rainfall, aerosols, dust, sand, micro- and macro-organisms and the mechanical deterioration of conductors. Based on the information provided above, the occurrence of PDs is the best indicator of overhead line faults [9, 12, 13].

The current worldwide research is focused on the development of methodologies for detecting the above mentioned faults in the operation of overhead lines with CCs. Most of these methodologies are based on evaluation of PD current pulses, and their selectivity and sensitivity depend on the measurement technique, which must meet high standards, especially the ability to detect pulse sources, and which must include a high-resolution A/D converter and efficient hardware for data processing [14−16].

The system developed by the team at VŠB-Technical University of Ostrava in the Czech Republic (hereinafter VŠB-TUO) and presented in this study, is able to specify the location and type of a fault [17, 18]. The system operation is based on analysing PD voltage signal pulses using suggested indicators of faults [9] and is not technically demanding.

2. Method’s principles

The method developed by the VŠB-TUO team is based on finding a relation between the occurrence and characteristics of PDs and the origin of faults in overhead lines with CCs. As was stated above, in the first part, the occurrence of PDs is characterized by damaging the insulation system of a variety of devices. These PDs arise in areas of small cavities in the insulation system as an effect of extreme local electrical tension. A simple model and substitution diagram of simulating the voltage and current conditions inside the insulation system is shown in Fig. 1.

Fig. 1. A simple model of an insulation system with a cavity [19].

A cavity capacitance (the damaged part of the insulation) is represented by C1, C2 is

a capacitance of the residual part of “healthy” insulation (a serial connection of C2 and C1), and C3 presents a significant capacitance of other parts of insulation. A sphere gap (SG) represents flashover in the cavity area and R is a resistivity of the discharge puncture after flashover on SG. When the insulation system is damaged and cavities inside it exist, the voltage on the cavity varies in time according to the formula:

278


)()(21

2

10tv

CC

Ctv

+

= , (1)

where v(t) is the power supply voltage. When the value of voltage on the cavity equals the

voltage ignition value, a PD occurs. These frequent PDs are superposed onto the carrier of capacitive current component.

2.1. Pulse component measurements

The basic part of capacitive current is caused by the supply voltage and for evaluation of PD activity it is not relevant. However, PDs superposed onto the carrier capacitive current, named

a pulse component, are very important for evaluation of PD activity inside the insulation system. Two basic methods can be used for indirect evaluation of PD activity:

i) evaluation of PD activity in the insulation system of CC by measuring the current signal

in CC by a Rogowski sensor [2], and ii) evaluation of PD activity in the insulation system of CC by measuring the voltage signal

of electrical stray field along the CC. Both methods use for evaluation of PD activity a pulse component. The pulse component

is generated by PD activity in the insulation system and its occurrence is characterized by

a frequency domain of hundreds of kH to MHz. The first method evaluates the pulse component generated by PD activity from the current measured by a Rogowski sensor. The main advantage

of this method is a high selectivity of evaluation of PD activity. However, this high selectivity of PD evaluation requires both high sensitivity and accuracy of the Rogowski sensor over a wide frequency range because the pulse component is low-energetic and the measurement

period is in the order of microseconds. These high requirements on the Rogowski sensor increase a price of the measurement chain, which is a great disadvantage of this method (i) [2].

The aim of this paper is to show the possibility of using the second method that evaluates the pulse component generated by PD activity as a voltage signal of the electrical stray field measured along an insulation system, in this case the insulation system of CC. The requirements

for development of this method were: high selectivity of fault detection, high reliability and a low price of the prototype CC fault detector.

As was stated in the previous section, the pulse component generated by PD activity in an insulation system of CC is measured as the voltage signal of electrical stray field along the CC. This voltage signal was measured by a capacitor voltage divider (CA-CB) from a circular metal

sensor (a circular coil; see Ccoil in Fig. 2) through its coupling capacitor Ccoup to the CC. As a sensor it is possible to use, for example, an inductor wound on the CC surface, where Ccoup

will be given by the number of turns (see Fig. 2).

Fig. 2. The principle of measuring the pulse component of voltage signal including an analogue low-pass filter.

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The time characteristic of voltage signal of the electrical stray field on the CC surface is then

amplitude-conditioned by means of a capacitor voltage divider with a fixed dividing ratio given by the capacities CA and CB; see Fig. 2. When the capacitor voltage divider is loaded via

a properly selected resistor R1, which may be additionally equipped with a self-inductance, a low pass with advantageous amplitude characteristic occurs; see Fig. 3 (the vertical axis –

a damping characteristic in dB, the horizontal axis – a frequency in Hz).

Fig. 3. Frequency characteristics of a coupling circuit in CC for various endings of the capacitor voltage divider

(C-divider, C-divider with R, C-divider with RL).

The voltage signal of the electrical stray field measured by the sensor as a function of time

is shown in Fig. 4, where the red line defines the output voltage signal using a C-divider and

the green line defines the output voltage signal using a C-divider with a resistor R1 connected in parallel. From the green line in Fig. 4, the required pulse component of voltage signal

generated by PD activity is visible. This signal can be filtered using a digital filter for elimination of the carrier frequency of power supply and for further specification of a typical

frequency range for PD activity (mostly 1−10 MHz). In this way, the original pattern of PD (hereinafter the PD-pattern) arises, corresponding to the actual state of CC insulation system. Next, detection of a CC fault is possible by evaluating this PD-pattern. It means that the shape

of the PD-pattern shows the actual state of CC insulation system. For evaluation of the PD-pattern it is possible to use some indicators in the time and frequency domain, whereas the

requirements for selection of the indicators are: (i) a short evaluation time; (ii) low memory requirements and (iii) selective evaluation.

Fig. 4. The functions of output voltage signal vs time using: a C-divider (red line), a C-divider with a resistor R1

connected in parallel for the no-fault state (green line), a C-divider with a resistor R1 connected in parallel

for a fault state (blue line).

280


So, for example, calculations of the True Root Mean Square value (hereinafter the TRMS) of the PD-pattern and the mean value of the PD-pattern or the frequency (s−1) of PDs in the PD-pattern (hereinafter n) for the first time were verified as indicators in evaluation of the actual state of CC insulation by the research team at VŠB-TU Ostrava. A function of the TRMS of PD-pattern (hereinafter VTRMS) vs time is approximately zero in the case of fault-free operation, because the PD activity is irrelevant (see the green line in Fig. 4). If a fault in the CC insulation exists, the PD activity is relevant and the TRMS value is increased; see the blue line in Fig. 4.

The next modification of the PD-pattern is extraction of a low-level PD signal from the background of an interfering signal source, which is composed of signal sources from the external environment (e.g. radio transmitters).

Therefore, to modify the electrical stray field voltage signal, we used an IIR Butterworth digital filter with an infinite pulse response and maximally flat permeable and impermeable ranges.

Based on the selected basic measurement system for recording and modifying the signal, we developed a fault-detecting system able to analyse the processed data, which is described in the following section.

3. Pulse component measurements

The main requirement for a fault-detecting system is the oscilloscopic measurement

of varying the PD-pattern voltage of electrical stray fields around medium-voltage overhead lines with CCs. We used a measuring card connected via a PCI interface for this purpose. In addition to measuring the PD-pattern, the fault detector measures other conditions, such as temperature, pressure, humidity and global radiation (exposure), since the discharge activity is affected by these factors. These conditions affect, for example, the frequency of PD occurrence, the PD amplitude shape and size .

All measured and processed data are sent by the GSM network to an external computer, where they are processed and an overhead line fault condition is analysed. If the threshold values of indicators are exceeded, the fault detector sends a warning signal to the CC operator.

The fault detector also includes additional control electronic circuits which are used to switch the PC to automatic control, and to measure temperature inside the switchboard (in the case of unnecessary heating). The device is powered by a battery which is charged by photovoltaic panels. Thus, it is possible to use the detector anytime on overhead lines with CCs, even when there is no possibility to get energy from the distributed system power supply.

4. Measurement of real medium-voltage overhead lines with CCs

4.1. Verification of fault detector function

The CC fault detector prototype was installed on 22-kV overhead lines with CCs (Fig. 5).

The main aim was to verify the effect of CC network topology on sensitivity and selectivity of the fault detector prototype and its long-term application in a chosen location with medium-voltage overhead lines.

To confirm the conclusions and to assess the fault detector functionality, experimental measurements were performed on real overhead lines with CCs (22 kV) in December 2012 and February 2013. The aim of measurements was to obtain new data and to verify the results already gained during the previous period, particularly setting the frequency threshold values (n = 100 s−1) and the voltage level of the generated PD voltage signal pulse component root-mean-square (VTRMS = 39 mV). The indicator n (s−1) is a frequency of PDs’ activity and, as well as VTRMS, was analysed during experimental measurements in the laboratory conditions [9, 13].

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When these values are exceeded, the fault detector sends a report about a fault in the

overhead lines. Different types of faults were simulated on overhead lines with CCs, particularly faults that cannot be detected by current digital relay protection systems. In particular, selectivity and sensitivity of both the methodology and fault detector were verified

for such faults as a contact between a tree branch and a phase conductor, a conductor falling on the ground and a contact between two phase conductors. Due to the insulation of conductors,

these faults do not have to be cleared immediately. However, the tested fault detector can detect these faults before degradation factors destroy integrity of the insulation in the fault location and cause a single phase-to-earth short-circuit.

Fig. 5. Arrangement of the fault detector on a post of medium-voltage overhead lines with CCs [21]:

MS − Measuring System, BAT − Battery, SM − Sensing Member, CD − C-Divider, PP − Photovoltaic Panel.

The results of these experimental measurements are presented below:

Fault no. 1 – the point of contact between a tree and CC; Fault no. 2 – breaking off of a CC and its subsequent falling on the ground.

To compare the faulty and fault-free conditions (Fig. 6), we had to measure the PD-pattern in the operating conditions. From the PD-pattern (Fig. 6), the existence of a pulse component is evident, although the overhead lines with CCs were free of fault generated by a corona

discharge at the connector endings on towers with CCs and also by modulation of interfering signals (e.g. radio waves). The software component of fault detection system can recognize

the interference and evaluate the signal as fault-free.

Fig. 6. The VTRMS of PD-pattern of CC for the no-fault state.

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Fault no. 1 – point of contact between tree and phase conductor.

The first measurement was simulation of the point of contact with a phase conductor. This fault was simulated by considering a tree branch located near the outer phase of CC (Fig. 7a). This type is the worst detectable fault because a contact between a tree and a conductor can, in

real situations, be a result of transitory conditions, e.g. wind. Another fact contributing to the difficulty in detecting this type of fault is the minimal area of conductor damage and the

corresponding minimal occurrence of PDs in the fault location. By further analysing the pulse component of the generated PD-pattern in the fault location, we determined the following

indicator values: n = 272 s−1; VTRMS = 68 mV. Considering the exceeded indicator threshold values, selectivity and sensitivity of the

methodology as well as the fault detector functionality were verified. Changing of the measured signal in time, shown below (Fig. 7b), clearly indicates that over a period of 0.06 s no PD

occurred. This lack of PD was caused by an imperfect connection between a tree branch and CC. The fault detector evaluates faults continually; therefore, this transient effect on the general

selectivity of fault detector is eliminated.

Fig. 7. Fault no. 1 – a contact between a tree branch and overhead lines with CC (a);

the change of PD-pattern in time, fault no. 1 (b).

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Fault no. 2 – breaking off of CC and its subsequent falling on ground.

The second simulated fault was the breaking off of a CC and the conductor’s subsequent falling on the ground. The fault was simulated by connecting an SAX-W-type conductor (22-kV) to the overhead lines. The CC end was then placed down on the ground (Fig. 8a). At the

point of contact between the conductor and the ground, PDs evolve and the voltage signal, which afterwards travels along the insulation of the conductor as a wave, is recorded by the

fault detector. This type of fault is easily detected; therefore, in the step the conductor was placed on the ground covered with grass. The contact with the ground was partly weakened by grass. Fig. 8b shows the PD-pattern recorded after using the IIR Butterworth filter; the measured

values were: n = 174 s−1 ; VTRMS = 68 mV.

Fig. 8. Fault no. 2 – falling of a CC on the ground (a); the PD-pattern, fault no. 2 (b).

To provide a general summary of the measured values, we created a table of climatic

conditions (Table 1) and a table of chosen fault indicators (Table 2). As shown in Table 1, the measurements were performed in unfavourable weather conditions. Thus, if the temperature

was approximately equal to zero and humidity was high, we presumed the occurrence of PD in overhead lines in the form of a corona. Coronas frequently occur in areas of high local electrical

gradients, where inhomogeneous electrical fields are generated, such as sharp edges, bushings, connectors and other construction parts of overhead lines. Table 2 shows that the highest

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frequency values n occurred during a contact between a tree branch and a phase conductor (fault

no. 1). The high values were caused mainly by the fact that tree bark was soaked with water; thus, when the conductivity increased, the PD activity increased as well. When the conductor fell on the ground, we presumed that the highest energy of the PD voltage pulses occurred; thus,

the VTRMS value was also the highest of all the measured values in this case.

Table 1. The measured values of climatic conditions.

Temperature of the surroundings (°C) 3,2

Humidity (%) 85,1

Dew point (°C) 1

Atmospheric pressure (hPa) 968.5

Global radiation (W.m-2) 0

Temperature in switchboard (°C) 5,4

Table 2. The values of frequency and VTRMS.

VTRMS (mV) n (s-1)

Operating condition 9 17

Fault no. 1 45 272

Fault no. 2 68 174

4.2. Long-term measurement of medium-voltage (22 kV) overhead lines with CCs

After long-term experimental measurements, the fault detector was put into operation on MV (22 kV) overhead lines with CCs. During its operation in May and October, the fault detector sent to the local CC overhead lines’ operator a warning report indicating that the

threshold values of indicators had been exceeded . In particular, the following values were

measured by the detector: n = 150 s−1 (150 > 100) and VTRMS = 42mV (42 > 39) of PD-pattern. At first, during May, the breakdown service of distribution system operator made a round along

MV overhead lines with CCs and detected a fault in a site at a 3 km distance from the detector. The breakdown service detected falling of a tree branch across three phases.

The observed values (VTRMS and n) were analysed step by step every day and the mean value of these data was evaluated at the end of individual month. Next, the tangent of these values was evaluated, too. The graphical output of this analysis for VTRMS and n can be seen in Fig. 9.

Fig. 9. Mean values of n and VTRMS of PD-pattern for individual months of the year.

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From these graphical outputs a decrease in PD activity after elimination of the fault is evident

until July. However, the second warning report was sent by the detector during October, when the threshold values (VTRMS and n of PD-pattern) were exceeded again. The breakdown service of distribution system operator made a round along MV overhead lines with CCs again.

However, no fault in CCs has been found. Nevertheless, the detector sent the warning report because the threshold values (VTRMS and n of PD-pattern) were exceeded. The PD-pattern from

the detector is shown in Fig. 10b (red line – left axis). Therefore, the breakdown service scanned the overhead lines with CCs in more detail using

a corona camera and detected a fault in the same place as the previous fault. A photo illustrating

the fault is presented in Fig. 10a. From this photo there is visible a damage on the CC surface. This damage was caused by the PD activity of the previous fault when a tree branch fell across

three phases. This fault was cleared by the breakdown service during May. However, the insulation system of CC at the contact point of a tree branch with the insulation system had already been degraded. This degradation of the insulation system stopped during the summer

months when high temperatures in the surroundings of CC caused “softening” of the insulation system and these small ruptures in the insulation system were eliminated. The opposite effect

was caused during the autumn and winter months when the insulation system dried out and became more brittle as a result of low temperatures and low values of relative humidity. Therefore, the PD activity increased and degradation of the insulation system increased. The

damaged line with CC was changed and − to prevent another similar accident − the trees in the area occupied by the MV overhead lines were trimmed. As a result, the PD activity (see Fig. 10b – green line – right axis) and monitored values (VTRMS and n of PD-pattern) decreased

immediately (see Fig. 9) after executing these corrective and preventive steps.

Fig. 10. The details of damage on a conductor in the measured location (a); the PD-pattern from the detector after

it sent a warning report (left axis − red line) and the PD-pattern from the detector after carrying out the corrective and preventive steps (right axis – green line) (b).

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5. Conclusion

A system for detecting faults in overhead lines with CCs was designed based on a methodology developed by the research team at VŠB-Technical University of Ostrava. Prior to the construction of the fault detector, a number of experimental measurements [7, 8] and mathematical calculations using non-linear multi-physical programs (Lab View, ATP-DRAW, ANSYS) were carried out. Based on the results of these measurements and mathematical simulations, a fault detector prototype was constructed. The detector’s functionality was tested by the long-term measurement of real MV overhead lines with CCs. During the measurement process, the performance of particular CC fault indicators defined in the research part of the project was gradually verified. Using these results, the evaluation component of calculating algorithm of the fault detector prototype was optimized. The fault detector was powered by storage batteries recharged by solar panels.

Based on the test results obtained for the fault detector by long-term measurements in real conditions, the ability of the detector to operate in the autonomous mode was successfully verified. The indicator threshold values applied to a signal on occurring a fault in MV overhead lines with CCs were specified. The fault detector is able to specify faults based on the measured threshold frequency values and the True Root Mean Square value of the electrical stray field voltage signal around the conductor. The fault detector recognizes faults in the overhead lines and sends a signal informing about the faults to the central computer. Further confirmation of the fault detector’s ability to detect faults was obtained when the fault detector was put into operation. When the overhead lines were checked, it was observed that the cause of the detected fault was a tree branch that had fallen across all three phases of the lines. The fault caused partial damage to the conductor insulation, but due to the timely warning, there was no inter-phase short-circuit. Thus, the faults could be cleared within a short time, and more serious damage that could possibly cut the power supply to consumers could be prevented. Moreover, the repair costs were reduced.

In this study, we not only achieved the project objectives of producing a fault detector prototype and verifying its performance, but we also gathered a significant amount of information about the discharge activity of various insulation systems in various climatic conditions. This information can be used in developing other methods of protecting CCs as well as all other types of outdoor overhead lines and cable lines, and even insulation systems of other devices. In the future research, we aim to enhance the measurement quality of the fault detector, so that it is able to specify the location and type of faults that are detected.

Acknowledgments

This study was carried out within the framework of the IT4 Innovations Centre of Excellence project, reg. no. CZ.1.05/1.1.00/02.0070, supported by the Operational Programme “Research and Development for Innovations” funded by Structural Funds of the European Union and the state budget of the Czech Republic and the project Opportunity for Young Researchers, reg. no. CZ.1.07/2.3.00/30.0016, supported by the Operational Programme Education for Competitiveness and co-financed by the European Social Fund and the state budget of the Czech Republic and project reg. no. SP2014/49.

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[13] Hashmi, G.M., Lehtonen, M., Nordman, M. (2011). Calibration of on-line partial discharge measuring system using Rogowski coil in covered-conductor overhead distribution networks. Science, Measurement & Technology, IET, 5(1), 5−13.

[14] Hashmi, G.M., Lehtonen, M. (2010). Effects of Rogowski Coil and Covered-Conductor Parameters on the Performance of PD Measurements in Overhead Distribution Networks. Int. J. Innovations Energy Syst. Power, 4(2), 14–20.

[15] Sudha, G., Valluvan, K.R. (2014). A novel approach to fault diagnosis of transmission line with Rogowski coil. International Review of Electrical Engineering, 9(3), 656−662.

[16] Isa, M., Elkalashy, N.I., Lehtonen, M., Hashmi, G.M., Elmusrati, M.S. (2012). Multi-end correlation-based PD location technique for medium voltage covered-conductor lines. IEEE Transactions on Dielectrics and Electrical Insulation, 19(3), 6215097, 936−946.

[17] Misak, S., Pokorny, V. (2015).Testing of a covered conductor's fault detectors. IEEE Transactions on Power Delivery, 30(3), 6957620, 1096−1103.

[18] Hamacek, S., Misak, S. (2013). Fault indicators of partial discharges in medium-voltage systems. Advances in Electrical and Electronic Engineering, 11(4), 284−289.

[19] Záliš, K. (2005). Částečné výboje v izolačních systémech elektrických strojů. 1st. ed. Praha: Academia.


_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Aug. 03, 2016; accepted on Jan. 14, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0031.


Index 330930, ISSN 0860-8229


APPLICATION OF IMPROVED ROBUST KALMAN FILTER IN DATA FUSION

FOR PPP/INS TIGHTLY COUPLED POSITIONING SYSTEM

Zengke Li, Yifei Yao, Jian Wang, Jingxiang Gao

China University of Mining and Technology, School of Environment and Spatial Informatics, Xuzhou, China ([email protected], [email protected], [email protected], [email protected], +86 516 8388 5785)

Abstract

A robust Kalman filter improved with IGG (Institute of Geodesy and Geophysics) scheme is proposed and used to resist the harmful effect of gross error from GPS observation in PPP/INS (precise point positioning/inertial

navigation system) tightly coupled positioning. A new robust filter factor is constructed as a three-section function

to increase the computational efficiency based on the IGG principle. The results of simulation analysis show that

the robust Kalman filter with IGG scheme is able to reduce the filter iteration number and increase efficiency. The

effectiveness of new robust filter is demonstrated by a real experiment. The results support our conclusion that the

improved robust Kalman filter with IGG scheme used in PPP/INS tightly coupled positioning is able to remove the ill effect of gross error in GPS pseudorange observation. It clearly illustrates that the improved robust Kalman

filter is very effective, and all simulated gross errors added to GPS pseudorange observation are successfully

detected and modified.

Keywords: PPP/INS tightly coupled positioning, robust filter, IGG scheme, Mahalanobis distance.


1. Introduction

Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) is being used more often for obtaining several high precision navigation data (position, velocity

and attitude) [1]. The past integration research has been performed in different application areas (i.e., monitoring, transportation, etc.). GPS provides highly accurate position and velocity results over extended periods in the GPS/INS integrated system, and short-term position,

velocity, and attitude values are provided by INS. The GPS-alone positioning is difficult in challenging environments due to weakness and blockage of signals. INS is a self-contained

velocity and attitude measurement system that does not require an external signal. Therefore, integration of GPS and INS provides enhanced performance in comparison with each individual system [2]. The Precise Point Positioning (PPP) using un-differenced carrier phase and

pseudorange observations has been developed recently, and is capable of obtaining positions with a centimetre precision in the static mode and sub-centimetre precision in the dynamic

mode. This is accomplished by using precise satellite orbits and clock correction products (e.g. the International GNSS Service) [3]. Some PPP and INS integration research results enable to obtain more accurate position and attitude values in the single receiver mode. With an aid

of INS aid cycle slip detection and repair methods for the un-differenced GPS/MEMS (Micro-Electromechanical Systems) INS integrated system are proposed. These methods are capable

of efficient cycle slip detection and repair, effectively increasing the positioning accuracy of the integrated system [4].

The key process between INS and other sensors in the integrated positioning system

is information fusion. During the kinematic positioning, GPS signals are prone to be disturbed

Z. Li, Y. Yao, et al.: APPLICATION OF IMPROVED ROBUST KALMAN FILTER …

by trees, buildings and other shelters. Thus, the performance of integrated positioning will be

seriously degraded because of the gross error from GPS observation in GPS challenging environments. A robust Kalman filter could be employed to reduce the effect of gross error in GPS observation. Many forms of robust Kalman filters have been proposed in the literature.

A robust Kalman filter has been researched in the last dozen or so years in different application fields, such as in-motion alignment of INS [5], SINS/SAR integrated system [6], real-time

estimation of satellite clock offset [7], precise point positioning (PPP) [8], and others. A robust Kalman filter using the Chi square test to detect outliers in measurement was proposed in [9]. The outlier judging index was defined as the square of the Mahalanobis distance between the

observed and predicted results. Based on the robust Kalman filter using the Chi square test, a robust Kalman filter improved with IGG (Institute of Geodesy and Geophysics) scheme is

proposed and applied in PPP/INS tightly coupled positioning to increase its computational efficiency. The new robust filter factor is constructed as a three-section function on the basis of IGG principle.

The paper is divided into 5 sections. Following this introduction, a PPP/INS tightly coupled positioning model is overviewed in Section 2. Section 3 presents the robust Kalman filter

improved with IGG scheme, and the simulation analysis corresponding to it. The field test results are then presented and analysed in Section 4, followed by a summary of the main conclusions.

2. PPP/INS tightly coupled positioning

2.1. PPP observation model

The observation models of un-differenced GPS pseudo-range, carrier phase and Doppler

measurements for PPP can be expressed as follows [10]:

1 1

1 1( )

s P PP c dt dt I T Mρ ε= + ⋅ − + + + + , (1)

2 2

2

1

2 12

2

( )s P P

fP c dt dt I T M

fρ ε= + ⋅ − + + + + , (2)

1 1

1 1 1 1( )

s Φ ΦΦ c dt dt I T N Mρ λ ε= + ⋅ − − + + + + , (3)

2 2

2

1

2 1 2 22

2

( )s Φ Φ

fΦ c dt dt I T N M

fρ λ ε= + ⋅ − − + + + + , (4)

1

1 1( )

s DD c dt dt I Tρ ε= + ⋅ − − + +

ɺ ɺ ɺ ɺɺ , (5)

2

2

1

2 12

2

( )s D

fD c dt dt I T

fρ ε= + ⋅ − − + +

ɺ ɺ ɺ ɺɺ , (6)

where: P, Φ and D are pseudo-range, carrier phase and Doppler observations, respectively; ρ

is a geometric distance between the receiver antenna and satellite phase centres; ρɺ is a

geometric range rate; c is the velocity of light in vacuum; dt and s

dt are satellite and receiver

clock errors, respectively; dtɺ and s

dtɺ are the satellite clock error drift and receiver clock error

drift, respectively; I and Iɺ are a first-order ionospheric delay and an ionospheric delay drift,

respectively; f1 and f2 are frequencies of the carrier phases 1

Φ and 2;Φ T and Tɺ are

290


a tropospheric delay and a tropospheric delay drift. Because the hydrostatic part of tropospheric

delay can be predicted using models, T represents the wet component of tropospheric delay;

PM and

ΦM are multipath errors of the pseudo-range and carrier phase measurements;

Pε ,

Φε

and D

ε are combination noise values of the pseudo-range, carrier phase and Doppler

measurements, and subscripts 1 and 2 refer to the observations at different frequencies. By using the high-accuracy GPS satellite orbit and clock products, the errors in the satellite

orbit and clock corrections can be significantly reduced. Other error sources including the satellite antenna phase centre offset, phase wind up, earth tide, ocean tide loading and

atmosphere loading can be removed by a correction model. The widely used ionosphere-free combination makes use of the GPS radio frequency’s dispersion property to mitigate the first-order ionospheric delay effect. The observation model of ionosphere-free combination can be

expressed as follows [11]:

2 2

1 2

1 22 2 2 2

1 2 1 2

( )if ifif s P P

f fP P P c dt dt T M

f f f fρ ε= − = + ⋅ − + + +

− −

, (7)

2 2

1 2

1 22 2 2 2

1 2 1 2

( )if ifif s if if Φ Φ

f fΦ Φ Φ c dt dt T N M

f f f fρ λ ε= − = + ⋅ − + + + +

− −

, (8)

2 2

1 2

1 22 2 2 2

1 2 1 2

( )ifif s D

f fD D D c dt dt T

f f f fρ ε= − = + ⋅ − + +

− −

ɺ ɺ ɺɺ , (9)

where a subscript if refers to the ionosphere-free combination observation.

Because the change of tropospheric delay is very slow, the tropospheric delay drift can be considered to be zero. The variables estimated in PPP resolution are: the three-dimensional position, receiver clock error, receiver clock error drift, zenith tropospheric delay, and

ionosphere-free combination ambiguity.

2.2. Tightly coupled dynamics model

The dynamics error model of PPP/INS integrated positioning for the Kalman filter is

constructed on the basis of INS error equations. The insignificant terms are neglected in the linear approximation process [12]. The error equations of INS navigation could be theoretically

expressed as [13]:

en

δ δ δ= − × +r ω r vɺ , (10)

ie en

(2 )δ δ δ= − + × − × +v ω ω v ψ f ηɺ , (11)

ie en

( )δ δ= − + × +ψ ω ω ψ εɺ , (12)

where: δ r , δv and δψ are position, velocity and orientation error vectors, respectively; en

ω

is an angular rate of the navigation frame with respect to the earth frame, and ie

ω is an angular

rate of the earth frame with respect to the inertial frame. The system dynamics error of PPP/INS

integration navigation is obtained by expanding the accelerometer bias error vector η and the

gyro drift error vector ε .

The dynamic behaviour of accelerometer bias error η and gyro drift error ε usually can be

modelled as a first-order Gauss-Markov process, which can be represented as follows [14]:

1

η

ηλ

= +ɺη η u , (13)

291


1

ε

ελ

= +ɺε ε u , (14)

where:ηλ and

ελ are correlation times for the accelerometers and the gyros, respectively;

ηu

and ε

u are white noise vectors of the accelerometer bias error and the gyro drift error,

respectively. The state dynamic equations of receiver clock, tropospheric delay and ionosphere-free

carrier ambiguity which are related to PPP can be written as [11]:

dt

dt dt uδ= +ɺ , (15)

dt

dt uδ

δ =ɺ , (16)

T

T u=ɺ , (17)

if NN u=ɺ , (18)

where dt

u , dt

uδ

, Tu and

Nu are white noise vectors of the receiver clock error, receiver clock

error drift, zenith tropospheric delay and ionosphere-free carrier ambiguity, respectively. According to the equations (10) to (18), the system dynamics model can be generalized in a

matrix and vector form:

= +X FX uɺ , (19)

wherein: X is an error state vector; F is a transition matrix and u is a process noise vector.

2.3. Tightly coupled observation model

The observation model of Kalman filter in PPP/INS integrated positioning is a vector

composed of the pseudo-range, carrier phase and Doppler difference between the GPS observation and INS prediction values [15]:

GPS INS

GPS INS

GPS INS

j j

j j

j j

P P

Φ Φ

D D

−

− = −

Z

⋮

, (20)

where: GPS

jP , GPS

jΦ and GPS

jD are ionosphere-free pseudo-range, carrier phase and Doppler

values of the jth satellite observed by GPS, respectively; INS

jP , INS

jΦ and INS

jD are ionosphere-

free pseudo-range, carrier phase and Doppler measurement values of the jth satellite predicted by INS with the satellite position and velocity information, respectively.

The variable form of tightly coupled observation equation for Kalman filter can be generalized in a matrix and vector form:

k k k= +Z H X τ , (21)

where: k

Z is an observation matrix; k

H is an observation equation coefficient matrix and τ is

a vector of the observation noise, assumed to be white Gaussian noise.

292


2.4. Tightly coupled positioning flow

Figure 1 shows a PPP/INS tightly coupled positioning system. INS mechanization is an algorithm that calculates the current position, velocity, and attitude solutions from the IMU

information. Exact satellite position and clock correction information is obtained from the precise orbit and clock products. The position and velocity outputs from the INS mechanization

are used to predict the pseudo-range, carrier phase, and Doppler measurements for GPS. After correcting the errors (i.e. satellite antenna phase centre offset, phase wind up, earth tide, ocean tide loading) in the raw GPS measurements, the difference value between the corrected pseudo-

range, carrier phase, and Doppler measurement results from PPP and the INS-predicted measurement results is input into the Kalman filter as the observation vector. The final position,

velocity and attitude are obtained by the filter fusion and update. Higher accuracy predictions of pseudo-range, carrier phase, and Doppler are input into the filter and compared with the traditional PPP algorithm without INS.

Fig. 1. A PPP/INS tightly coupled positioning system.

3. Robust Kalman filter with IGG scheme

3.1. Kalman filter

When GPS is available, the Kalman filter estimation will be employed to update the state

parameters by time and observation updates in PPP/INS tightly coupled positioning. The time update process is expressed as:

, 1 1ˆ

k k k k− −

=X F X , (22)

T

, 1 1 , 1 1k k k k k k k− − − −

= +P F P F Q . (23)

The observation update equation of Kalman filter is written as:

k k k k= −V Z H X , (24)

T

kk k k k

= +VP H P H R , (25)

T -1

kk k k=

VG P H P , (26)

293


ˆk k k k= +X X G V , (27)

( )k k k k= −P I G H P , (28)

where: k

X is an a priori state estimation; ˆk

X is an a posteriori state estimation; k

G is a gain

matrix of Kalman filter; k

P is an a priori covariance matrix of the state vector; kP is an a

posteriori covariance matrix of the state vector; k

R is a covariance matrix of the observation

noise vector; 1k−

Q is a covariance matrix of the process noise, a subscript k denotes a moment,

and a subscript -1k,k represents the state or covariance estimates in a period between k-1 and

k moments.

In a closed loop integration scheme, a feedback loop is used for correcting the systematic errors of INS. In this way, the assumption of small errors can be employed [16]. Thus, an a posteriori state estimate is expressed as:

( )-1

T Tˆk k k k k k k k= +X P H H P H R Z . (29)

In a closed loop, the a posteriori state estimation will be used for correcting the positioning

parameters which set the a priori state estimation k

X to zero in the next filter prediction.

3.2. Robust Kalman filter based on Mahalanobis distance

Under the Gaussian assumption, k

Z should obey a Gaussian distribution with mean k

H X

and covariance k

VP . Therefore, the squared Mahalanobis distance of

kZ should be a Chi square

distribution [17], and its freedom is equal to the number of dimensions for the observation

vector:

( ) ( ) ( )-1T

2 2~

kk k k k k k m

Mγ χ= = − −V

Z H X P Z H X , (30)

where k

M is the Mahalanobis distance.

In order to find whether there is gross error in an observation k

Z , a Chi square test is formed

to determine whether the actual observation k

Z obeys a Gaussian distribution. A significant

level α, the probability threshold below which the null hypothesis will be rejected, is selected.

In this contribution 1% is adopted, and the corresponding upper α-quantile is 2

,m αχ :

2

,Pr

k m αγ χ α > < , (31)

where Pr[·] represents the probability of a random event. According to the law of Chi square

distribution, the probability of k

γ being larger than 2

,m αχ should be minute. Therefore, if the

actual k

γ is larger than this α-quantile, the basic assumptions are very likely incorrect, which

means that the observation is profoundly more likely disturbed by gross error.

If the index k

γ is larger than 2

,m αχ , a robust factor β is introduced to inflate the covariance

matrix of measurement noise vector:

k k kβ=R R . (32)

The robust factor is calculated as:

2

,

k

k

m α

γβ

χ= . (33)

294


According to the above method, when k

γ is larger than 2

,m αχ , the observation

kZ is

presumed to be disturbed by gross error.

3.3. Robust Kalman filter improved with IGG scheme

In the above robust Kalman filter, only one threshold value is used to identify whether the observation is with gross error or not. If the observation is disturbed by gross error, the robust

factor β is calculated to implement the robust filter algorithm. In the engineering projects, the

observation usually is disturbed by different levels of gross error. If the gross error is small, the observation will play a part role in the filter update by expanding the covariance matrix of measurement noise vector. If the gross error is large, the observation is of no any positive

effect. In that case, the covariance matrix of measurement noise vector can be directly set to infinity to remove the negative effect of observation with gross error. So an improved robust

Kalman filter is constructed by adding a new robust factor with IGG scheme to improve the calculation efficiency using a piecewise function [18]:

0

0 1

1

2

,

2 2

, ,2

,

2

,

1k m

k

k m k m

m

m k

α

α α

α

α

γ χ

γβ χ γ χ

χ

χ γ

≤

= < ≤ ∞ <

. (34)

The probabilities 0α and

1α are set to 1% and 0.01%, respectively. If the actual

kγ is larger

than this 1-quantileα , the equivalent covariance matrix

kR is set to ∞ rather than iteratively

computed. The stage of detecting a gross error is slightly more complex and the computational

efficiency is increased. Comparing the above with a plain robust Kalman filter, the main difference is in the condition when the gross error is large. An easier algorithm will be implemented and a higher efficiency will be achieved in this situation for the improved filter.

3.4. Simulation analysis

The two-dimensional kinematic positioning simulation with a constant velocity is employed. The dynamic model can be written as:

N N

E E

N N N

E E E

00 0 1 0

00 0 0 1

0 0 0 0

0 0 0 0

p p

p p

v v

v v

α

α

= = +

= +

X

ΦX u

ɺ

ɺɺ

ɺ

ɺ

, (35)

where N

p , E

p , Nv and

Ev are positions and velocities in the north and east directions,

respectively, Nα and

Eα are the north and east accelerations, which are considered random

noise in the constant velocity model. A discrete time form of the dynamical model is as follows:

, 1 1k k k k k− −

= +X F X u . (36)

The simulation test’s observation data are positions in the north and east directions, so the observation model of Kalman filter is:

295


N

E N

N E

E

1 0 0 0

0 1 0 0

k k k k

p

p

v

v

τ

τ

+

= +

=

Z H X τ

. (37)

The process noise u and observation noise τ obey a Gaussian distribution. The standard

deviations of process noise and observation noise are set to 0.15 m/s2 and 1 m, respectively. The gross error case is studied to compare the performance of different construction methods

of the robust factor. In the gross error case, gross errors with values of 5 m, 8 m and 20 m are added into the position observations in the north and east directions every 100 s, 200 s and 300 s, respectively, and a standard Kalman filter (scheme 1), a robust Kalman filter (scheme 2) and

a robust Kalman filter with IGG scheme (scheme 3) are employed.

Figure 2 shows the values of judgment statistic k

γ . The red and green lines represent the

threshold values (9.2 and 18.4) of significance levels 0α and

1α , respectively. There are 28

values of k

γ which are less than 18.4 and greater than 9.2 and 28 values of k

γ which are greater

than 18.4. Different strategies using the IGG scheme are employed to process the various levels of gross error. The position error series for different schemes is plotted in Fig. 3. The RMSs

of position errors for three schemes are illustrated in Table 2. The position error for a standard Kalman filter is large due to the fact that gross errors with values of 5 m, 8 m, and 20 m are added to the position observation. As expected, both scheme 2 and scheme 3 show a very similar

robust performance. The position error of scheme 2 is somewhat larger than the position error of scheme 3, which demonstrates that the robust Kalman filter with IGG principle achieves

a better performance. Fig. 4 shows the filter iteration numbers for schemes 2 and 3 when gross error occurs. The sum total of filter iteration numbers for scheme 2 is greater than that for scheme 3. The filter iteration numbers of schemes 2 and 3 for the situation with gross error are

1391 and 983, respectively. Scheme 3 achieves nearly the same performance as scheme 2 and even a slightly better efficiency than scheme 2. In conclusion, scheme 3 achieves a better

performance and a higher efficiency than scheme 2.

Fig. 2. The value of judgement statistic for gross error.

0 500 1000 1500 2000 2500 30000

10

20

30

time (s)

γk

value of judgment statistic

296


a) b) c)

Fig. 3. Position errors for different schemes without gross error:

a standard Kalman filter (a); a robust Kalman filter (b); an improved robust Kalman filter (c).

Fig. 4. The filter iteration numbers for different schemes with gross error.

Table 1. Comparison of RMSs for different schemes regarding a position error.

Scheme North (m) East (m)

Standard filter 0.955 0.968

Robust filter 0.654 0.653

Improved robust filter 0.651 0.649

4. Field test and analysis

A field test with one MEMS grade IMU (Inertial Measurement Unit), one tactical grade

IMU, and two GPS receivers was performed on the roof of the Nottingham Geospatial Institute (NGI), and its intent was to validate performance of the proposed filter method. Initially, one Leica AS10 GNSS dual-frequency antenna was installed on the top of a pillar above the NGI

locomotive. The MEMS IMU, connected to the Leica antenna, recorded raw observations onto an SD card for post-processing from inside the locomotive. The reference station consisted

of another GPS receiver placed on one of the NGI roof pillars. Sampling rates of GPS receivers and IMU were set to 10 Hz and 200 Hz, respectively. The sky plots (azimuth vs. elevation) of GPS at the moving station are shown in Fig. 5. Observations from PRN3, PRN7, PRN8,

PRN16, PRN18, PRN19, PRN21, PRN22 and PRN27 during the field test were available.

0 500 1000 1500 2000 2500 3000-10

-5

0

5

10

no

rth

(m

)

position error of standard Kalman filter

0 500 1000 1500 2000 2500 3000-10

-5

0

5

10

time (s)

east

(m

)

0 500 1000 1500 2000 2500 3000-10

-5

0

5

10

no

rth

(m

)

position error of robust Kalman filter

0 500 1000 1500 2000 2500 3000-10

-5

0

5

10

time (s)

east

(m

)

0 500 1000 1500 2000 2500 3000-10

-5

0

5

10

no

rth

(m

)

position error of improved robust Kalman filter

0 500 1000 1500 2000 2500 3000-10

-5

0

5

10

time (s)

east

(m

)

0 500 1000 1500 2000 2500 30000

10

20

30

40

time (s)

number

filter iteration number

standard filter improved robust filter

297


Fig. 5. Sky plots (azimuth vs. elevation) of GPS at the moving station.

The entire test was completed in approximately 20 minutes. The GPS software, GrafNavTM 8.0, was used to process GPS observation in the DGPS mode, and the solution was regarded as

the position and velocity reference. The Inertial Explorer processing software generated the attitude reference using observations from two GPS receivers and one tactical grade IMU. The root mean square (RMS) error is used based on the reference value to obtain accuracy

of different schemes. Fig. 6 presents the experience trajectory and the devices used during the test. Table 2 provides specifications of the MEMS-IMU.

GPS reference station

Locomotive

Fig. 6. A field test.

Table 2. The MEMS grade IMU technical data.

Parameters Gyroscope Accelerometer

Initial bias error ±0.25º/sec ±0.002 g

In-run bias stability 18º/hr ±0.04 mg

Scale factor stability ±0.05% ±0.05%

Random walk 0.03º/s/sqrt (Hz) 80 µg/sqrt (Hz)

In order to test performance of a robust Kalman filter in PPP/INS tightly positioning, the gross error case is studied, and a standard Kalman filter (scheme 1), a robust Kalman filter

(scheme 2) and an improved robust Kalman filter (scheme 3) are employed. Gross errors with

values of −20 m, −15 m, and 20 m were added to the pseudo-range observation on PRN7,

PRN18, and PRN22 every 100 s, respectively. Gross errors with values of 10 m, −5 m, and 15 m were added to the pseudo-range observation on PRN3, PRN21, and PRN27 every 80 s, respectively.

298


In Fig. 7 field test trajectories for different schemes are compared. Fig. 8 shows the time

series of position errors in the north, east and down directions for scheme 1, scheme 2 and scheme 3. The RMSs of position errors of three schemes are presented in Table 3. Fig. 9 shows a histogram of position errors’ RMSs in the north, east and down directions for schemes 1, 2

and 3. The positioning resolution trajectory by the standard Kalman filter seriously deviates from the reference. Similarly to the simulation analysis results, accuracies of schemes 2 and 3

are again almost of the same quality. So the field test trajectories and position error curves from schemes 2 and 3 almost coincide. Scheme 3 achieves nearly the same performance as scheme 2 and even a slightly better efficiency than scheme 2 from the statistical result of RMS, which

is also similar to the simulation test results. The improved robust Kalman filter is able to remove the ill effect of gross error. The RMSs of position errors in the north, east and down direction

are 0.695 m, 0.875 m and 0.548 m, respectively, when the standard Kalman filter is used. However, the RMSs of position errors are 0.465 m, 0.524 m and 0.293 m, respectively, when the improved robust Kalman filter is applied. In comparison with scheme 1, the improvements

are about 33%, 40% and 47% for using scheme 3 in the north, east and down directions, respectively. The position RMS of scheme 3 is 0.759 m which is better than that of scheme 1

with an improvement of 39% in the three-dimensional component. It clearly illustrates that the robust Kalman filter with IGG scheme is very effective, and all gross errors are successfully identified. Significantly, there are obvious improvements for PPP/INS tightly coupled

positioning if a robust Kalman filter with IGG scheme is used. IGG scheme can be used as a very efficient filtering tool.

Fig. 7. Field test trajectories for different schemes with gross error.

Fig. 8. Position error series for different schemes with gross error.

-1.1842 -1.1840 -1.1838 -1.1836 -1.183452.9518

52.9519

52.9520

52.9521

longitude/(°)

latitude/(°)

trajectory

standard filter

robust filter

improved robust filter

reference

486100 486300 486500 486700 486900 487100-6

0

6

north/m

position error

486100 486300 486500 486700 486900 487100-6

0

6

east/m

standard filter robust filter improved robust filter

486100 486300 486500 486700 486900 487100-6

0

6

time/s

down/m

299


Fig. 9. Comparison of position errors for different schemes with gross error.

Table 3. Comparison of RMSs for different schemes regarding a position error.

Scheme North (m) East (m) Down (m)

Standard filter 0.695 0.875 0.548

Robust filter 0.481 0.527 0.293

Improved robust filter 0.465 0.524 0.293

5. Conclusions

During the robust filter process, iterative computations will take much time, thus reducing the computational efficiency. To increase it, an improved robust scheme is proposed based on

the robust Kalman filter with Mahalanobis distance and a new robust filter factor is constructed as a three-section function using the IGG principle. By simulation and comparing errors obtained for a standard Kalman filter, a robust Kalman filter based on Mahalanobis distance

and an improved robust Kalman filter with the IGG principle, the improved robust Kalman filter provides the best performance and fewer filter iteration numbers than the robust Kalman

filter based on Mahalanobis distance. A PPP/INS tightly coupled positioning experiment was carried out to further validate the

performance of the proposed filtering method. The position accuracy for PPP/INS integrated

positioning can be degraded by the gross error in GPS observation. The improved robust Kalman filter with the IGG principle was employed in PPP/INS tightly coupled positioning to

remove the harmful effects from gross error of GPS pseudorange observation. Compared with the standard Kalman filter, the improved robust Kalman filter accuracy regarding the east, north

and down components can be improved by 33%, 40% and 47%, respectively. The improved robust Kalman filter is very effective in identifying a simulated gross error added to GPS pseudo-range observation, which proves its good performance.

Acknowledgements

The work was partially sponsored by China’s Post-doctoral Science Fund (grant number:

2015M580490) and partially sponsored by Natural Science Foundation of Jiangsu Province (grant number: BK20160247). The authors would like to thank Dr. Xiaolin Meng and all experienced members in the University of Nottingham for their help in collecting and

processing the field test data.

North East Down0

0.5

1

direction

error/m

position error

standard filter robust filter improved robust filter

300


References

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urban areas. Sensors, 13(9), 11280−11288.

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Applications. Ph.D. Thesis. The University of Calgary.

[3] Kouba, J., Héroux, P. (2001). Precise point positioning using IGS orbit and clock products. GPS Solut., 5(2),

12−28.

[4] Du, S., Gao, Y. (2012). Inertial aided cycle slip detection and identification for integrated PPP GPS and INS.

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navigation system. Measurement, 42(4), 577−582.

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system. Aerosp. Sci. Technol., 15(6), 425−430.

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filter with classified adaptive factors. GPS Solut., 16(4), 531−539.

[8] Guo, F., Zhang, X. (2014). Adaptive robust Kalman filtering for precise point positioning. Meas. Sci.

Technol., 25(10), 1−8.

[9] Chang, G. (2014). Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion. J.

Geod., 88(4), 391−401.

[10] Du, S. (2010). Integration of precise point positioning and low cost MEMS IMU. Ph.D. Thesis. The

University of Calgary.

[11] Abdel-salam, M.A. (2005). Precise point positioning using un-differenced code and carrier phase

observations. Ph.D. Thesis. The University of Calgary.

[12] Titterton, D. (2004). Strapdown inertial navigation technology. 2nd ed. MIT Lincoln Laboratory.

[13] Han, S., Wang, J. (2012). Integrated GPS/INS navigation system with dual-rate Kalman Filter. GPS Solut.,

16(3), 389−404.

[14] Li, Z., Wang, J., Li, B., Gao, J., Tan, X. (2014). GPS/INS/Odometer integrated system using fuzzy neural

network for land vehicle navigation applications. J. Navigation, 67(6), 967−983.

[15] Zhang, Y., Gao, Y. (2008). Integration of INS and un-differenced GPS measurements for precise position

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[18] Yang, Y. (1994). Robust estimation for dependent observations. Manuscripta Geodaetica, 19(1), 10−17.


_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Aug. 15, 2016; accepted on Jan. 28, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0035.



ASSESSMENT OF FREE-FORM SURFACES’ RECONSTRUCTION ACCURACY

Artur Wójcik1), Magdalena Niemczewska-Wójcik2), Jerzy Sładek2)

1) University of Agriculture in Cracow, Department of Mechanical Engineering and Agrophysics, Balicka 120, 30-149 Cracow, Poland ( [email protected], +48 12 662 4678) 2) Cracow University of Technology, Faculty of Mechanical Engineering, Jana Pawła II 37, 31-864 Cracow, Poland ([email protected], [email protected])

Abstract

The paper presents the problem of assessing the accuracy of reconstructing free-form surfaces in the

CMM/CAD/CAM/CNC systems. The system structure comprises a coordinate measuring machine (CMM) PMM

12106 equipped with a contact scanning probe, a 3-axis Arrow 500 Vertical Machining Center, QUINDOS

software and Catia software. For the purpose of surface digitalization, a radius correction algorithm was

developed. The surface reconstructing errors for the presented system were assessed and analysed with respect to

offset points. The accuracy assessment exhibit error values in the reconstruction of a free-form surface in a range

of ± 0.02 mm, which, as it is shown by the analysis, result from a systematic error.

Keywords: reverse engineering, accuracy assessment, free-form surface, coordinate measuring machine, radius

correction


1. Introduction

The measurement method based on CMM technology has found widespread use in those areas of industry which require high accuracy and reliability of measurement, or to which other methods cannot be applied due to the nature of measurement, e.g. in measuring free-form

surfaces within the scope of industrial design. In this case, an initial design of such products is entrusted to craftsmen who construct the first physical model (a reference object) of the

structure of a designed product. Naturally, the design consists of far more complicated forms

than simple regular shapes − such as spherical, cylinder, or conic ones − which are not explicitly described in mathematical terms. The subsequent stages of design involve making a digital

cloud of points of the reference object and creating a prototype from a material suitable for manufacturing of, e.g., injection moulds. For this purpose, it is necessary to create an integrated system comprising tools for measurement, analysis, and manufacturing. These issues fall within

the area of widely-understood reverse engineering (RE) [1, 2]. In this process (RE) errors not only result from many factors related to digitizing, CAD/CAM

modelling, and manufacturing processes (CMM/CAD/CAM/CNC), but also are being induced by the applied machine tools and measuring strategies. This problem has been comprehensively

analysed in many papers [3−6].

The paper focuses on presentation of a method developed for creating a free-form surface of a reference object, along with its digitizing using a coordinate measuring machine (CMM). Next, it creates a free-form surface copy and evaluates reconstruction errors of the

CMM/CAD/CAM/CNC system (Fig. 1). The digitizing process was carried out with a CMM equipped with a contact scanning probe.

A surface made of aluminium (AlZnMgCu0.5) was examined. For the purposes of the described

A. Wójcik, M. Niemczewska-Wójcik, J. Sładek: ASSESSMENT OF FREE-FORM SURFACES’ …

system, a method including software for probe tip radius correction in reference to free-form

surfaces was developed. The applied procedure is shown in Fig. 1.

Fig. 1. A workflow of the proposed procedure.

The paper does not put emphasis on analysing the impact of individual error-inducing factors

on the final results, treating the system as a whole. The obtained results, therefore, should be perceived as attainable accuracy of the presented CMM/CAD/CAM/CNC system used for the

reconstruction of a free-form surface from readings taken from a reference object.

2. Probe tip radius correction and measurement strategy

Coordinate measuring machines with contact scanning probes enable to inspect practically any free-form surface. Admittedly, their capability of continuous-contact scanning with the

highest possible degree of accuracy offer a huge advantage. However, the key issue that needs to be tackled in the context of free-form surfaces is radius correction of an indicated measured

point set in the centre of stylus tip in relation to the corrected measured point (Fig. 2). Since a measured surface lacks a mathematical representation, determination of the tip correction vector will always bound to be approximate, i.e. encumbered with an error.

Fig. 2. The idea of coordinate measurement; the principle of probe tip radius correction (a);

measurement by means of CMM (b).

304


This issue has been discussed at length in the literature. The methods of probe tip radius

correction may be grouped into several areas. One of them is approximation of a cloud of points obtained from scanning a surface with the use of sets of mathematical formulas, most often B-

spline functions or others [7]. This approach is commonly known as the least-squares method [8]. However, this leads to averaging the values of respective measuring points, which adversely

affects the accuracy of the reconstruction of a measured surface. In another method of probe radius compensation there are determined normal vectors, drawn in the positions

of neighbouring measuring points [9−11].

A fundamentally different approach has been offered by Wozniak et al.; they use an algorithm which does not calculate the probe tip radius correction vector, but directly determines adjusted measuring points. This approach is based on fuzzy logic algorithms [12]

and a geometric method [13]. For the purpose of probe tip radius correction and finding a vector normal to the surface at

a given point, it is possible to employ a method analysing force distribution in the transducer of an active probe head [14].

In order to avoid errors resulting from the probe tip radius correction in accuracy assessment

on the basis of a CAD model, measurements can be performed without that correction. In this case the indicated measured points are compared with points distributed on an off-set surface

in a stylus tip radius distance from the CAD model in the normal direction [15]. Taking into consideration that not every computer program running on CMMs has separate

modules for probe tip radius correction in reference to free-form surfaces and bearing in mind that the tip radius compensation algorithm does not produce expected results, in this work a computer software used for probe tip radius correction has been developed. The input data for

the presented stylus tip radius correction method is a grid of points (the indicated measured points) displaced from the reference object by a length of the stylus ball radius. The algorithm

is based on determination of vectors starting from a given indicated measured point and pointing to all neighbouring points as well as being based on indication of a normal vector for each of the

determined vector pairs. The normal vector is estimated by a mean vector determined from a bunch of vectors starting from an indicated measured point (Fig. 3). What provides a distinct advantage of the presented solution is that the selection of an appropriate measuring strategy

ensures satisfactory results and may be used for any cloud of points grouped in the measuring paths.

Fig. 3. The strategy of determining the direction of the probe tip radius correction vector.

With the view of verifying the developed method, a set of reference spheres with known

diameters were measured. In the first place, the radii of the spheres and sphericity deviations

305


were determined with the use of a coordinate measuring machine PMM 12106. The obtained

values are compiled in Table 1. Then, the upper surfaces of spheres were scanned (a point

density of 0.5 × 0.5 mm) using a scanning head with a tip radius of 1.5 mm. The indicated measured points were subjected to stylus tip radius correction. Each corrected measured point

was compared with its corresponding point calculated using an analytical spherical function (partial derivatives). The distance between these points was regarded as an error of the

correction method. Table 1 displays the average error values calculated for all the points. Verification of the method showed that it brought satisfactory results, especially for surfaces

with a larger radius of curvature.

Table 1. The accuracy of the tip radius correction method [mm].

radii of the spheres [mm] sphericity deviations [mm] average error of the correction

method [mm]

4.7631 0.0010 0.0120

7.1446 0.0011 0.0067

12.7007 0.0011 0.0046

17.4636 0.0008 0.0028

25.4015 0.0017 0.0017

50.0059 0.0023 0.0009

After analysis of the results, it may be inferred that an error of the presented probe tip radius

correction method depends on the radius of curvature. Due to the fact that the radii of the

measured surface curvatures were greater than the radius of the largest sphere and owing to a higher point density in the measuring path during scanning, it was concluded that the accuracy

of the probe tip radius correction method was sufficient.

3. Accuracy assessment methodology of milled free-form surface reconstruction using

developed probe tip radius correction method

3.1. System structure and tools

The examined system structure consisted of the following components (Fig. 4):

− a laboratory version of coordinate measuring machine PMM 12106 equipped with a contact scanning probe;

− a 3-axis Arrow 500 Vertical Machining Center fitted with ACRAMATIC 2100E control;

− a high-speed spindle TDM, enabling machining at a maximum speed of 40,000 rev/min (High Speed Cutting);

− software: QUINDOS, Catia.

Fig. 4. The system structure.

306


3.2. Digitizing and manufacturing

In order to test the adopted method, a surface containing concave and convex curvatures was

used as the reference object. This object was treated as a material of standard size; the accuracy of reconstructed items was meant to be referred to it. The first step in research was to create

a digital cloud of points of the reference object. It was made with the use of a coordinate measuring machine PMM 12106 equipped with a contact scanning probe. Measurement of the reference object was made in the continuous scanning mode. A distance between the paths was

set to 0.5 mm, whereas a density of points in the path was set to 3 points/mm. The points which were obtained from surface scanning were subjected to the stylus tip radius correction, as it was

described in Section 2 (Fig. 5). A length of the correction vector is the effective radius of the probe tip, which comes from a qualification procedure before measurement. When measurements were carried out with a contact probe terminated with a ball stylus tip, the

measuring devices collected points separated with a fixed distance from the actual surface. The tip radius correction enabled to obtain corrected points representing actual (approximate) copies

of the reference object surface, which became the basis for generating a machining program on a CNC milling machine. The copy of the reference object was manufactured using a monolithic

ball-nosed milling cutter with a diameter of 8 mm, on a 3-axis Arrow 500 Vertical Machining Center fitted with ACRAMATIC 2100E control.

Fig. 5. Measurement of points before and after the probe tip radius correction.

4. Assessment of reconstruction accuracy

Regarding evaluation of the reconstruction accuracy, the indicated measured points obtained

during digitization of the reference object copy were subjected to examination. The indicated

measured points of the reference object were used as input points to control the measuring process of its copy. From a measurement point of view, it was recommended to probe the area

in the normal direction. To determine the normal vector, the software dedicated to probe tip radius correction was used, which additionally calculated the normal versor for every single

indicated measured point. Fig. 6 presents a window of the measuring mode from Quindos software.

307


Fig. 6. A window of the measuring mode from Quindos software.

The input points (the indicated measured points from the reference object) were imported to

Quindos metrology software cooperating with a CMM. The prepared input data, after setting the local coordinates, enabled to measure the reference object copy in the automated mode.

Comparison between the coordinates of points obtained from the performed measurements

and the (input) measured points enabled to determine a map of errors. In the ideal case, measurement should be taken in the same point. In order to minimize the impact of stress change

within the measured surface, a constant contact force in the vices of the machine tool and the measuring machine was applied. Fig. 7 shows graphical interpretations of reconstruction error

calculation for each measured point.

Fig. 7. The principle of determining a reconstruction error in a point.

A mapping error is determined by the following equation:

, , ,

, , ), (1)

308


where:δ – a reconstruction error in a point; , , – x, y, z error components; (x, y, z) – an

indicated measured point of the reference object; (x’, y’, z’) – an indicated measured point of the reference object copy.

According to the formula (1), the error values (δx, δy, δz) were calculated. Fig. 8 shows

a spatial distribution of the individual x, y, z error components across the surface.

Fig. 8. Reconstruction errors [µm]: a 3D surface profile (a); the values of x component of the error (δx) (b);

the values of y component of the error (δy) (c); the values of z component of the error (δz) (d).

From a preliminary analysis of the obtained results, it may be concluded that a significant

share in a vector error value has its z component. Therefore, mainly this component was subjected to analysis in further research.

5. Analysis of errors in selected surface profiles

Further error analysis was carried out for selected profiles, characteristic for this surface.

Fig. 9 shows the error values for the z component. As it has been already mentioned, finding the origin of errors in such a complicated system

as CMM/CAD/CAM/CNC is very complex. Errors result from a variety of factors which, if acting together, may add up or, which is even more difficult to capture, may compensate each other.

It may be expected, however, that if the measuring-manufacturing system is stable (repeatable), it will be generating errors of a specific character, dependent on the curvature of an

analysed surface. In order to capture potential regularities, errors in selected (specific) cross-sections of the surface were analysed (Fig. 9). From the analysis of selected curvature profiles,

309


it was concluded that if the cutter axis was perpendicular to the plane tangent to the surface,

an error in the direction of z axis amounted to approx. +0.020 mm, (Fig. 9, Fig. 11a). The analysis also showed that this error decreased with increasing inclination of the plane tangent

to the surface profile until it reached a value of 0 mm at the inclination angle of about 50º (Fig. 9, Fig. 11b). At a greater angle of inclination, the absolute error value increased again, taking

negative values (Fig. 9, Fig. 11c).

Fig. 9. The values of δz error components for respective surface profiles; the reference object (a);

the profile and δz error components for the cross-sections: (A-A), (B-B), (C-C), (D-D).

Fig. 10. The sources of surface reconstruction errors.

310


Fig. 11. The contact of the cutter with the machined surface.

A conclusion from the above considerations is that, if such a relationship reoccurs, it must be resulting from a strong (regular) factor, which in turn might be eliminated, e.g. at the level of software controlling the CNC machine.

6. Summary

The proposed method makes it possible to assess the reconstruction accuracy of complex-shaped products. It can be used along with the developed software as an effective tool

supporting the work of constructors and technologists in designing and manufacturing of complex-shaped products limited by free-form surfaces (in RE).

The points in which measurement is performed result from scanning a reference object. An advantage of the proposed method is that there is no need to make another probe tip radius

correction, which would contribute to further accumulation of errors. The probe tip radius correction is performed only once in order to manufacture a copy of the reference object. Regarding reconstruction accuracy assessment, both the indicated measured points obtained

from scanning the reference object and normal versors are used, the latter calculated with the use of the developed correction method. The presented method was verified for a free-form

surface reference object. The results showed that the reconstruction errors of the reference object exhibited values in a range of ±0.02 mm, which, as it is obtained from the analysis,

resulted from a systematic error.

Acknowledgments

This Research was financed by the Ministry of Science and Higher Education of the Republic

of Poland

References

[1] Li, Y., Gu, P. (2004). Free-form surface inspection techniques state of the art review. Comput. Aided. Des.,

36, 1395–1417.

[2] Werner, A., Skalski, K., Piszczatowski, S., Świeszkowski, W., Lechniak, Z.(1998). Reverse engineering of

free-form surfaces. J. Mater. Process Technol., 76(1–3), 128–132.

[3] Sladek, J.A. (2016). Coordinate Metrology Accuracy of Systems and Measurements. Springer-Verlag Berlin

Heidelberg.

[4] Poniatowska, M. (2008). Determining uncertainty of fitting discrete measurement data to a nominal surface.

Metrol. Meas. Syst., 15(4), 595–606.

[5] Poniatowska, M. (2012). Deviation model based method of planning accuracy inspection of free-form

surfaces using CMMs. Measurement, 45, 927–937.

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[6] Poniatowska, M. (2015). Free-form surface machining error compensation applying 3D CAD machining

pattern model. Comput. Aided. Des., 62, 227–235.

[7] Zhongwei, Y., Yuping, Z., Shouwei, J. (2003). Methodology of NURBS surface fitting based on off-line

software compensation of errors of a CMM. Precis. Eng., 27, 299–303.

[8] Xiong, Z., Li, Z. (2003). Probe radius compensation of workpiece localization. J. Manuf. Sci. Eng., 125,

100–104.

[9] Lee, R.T., Shiou, F.J. (2010). Calculation of the unit normal vector using the cross-curve moving mask

method for probe radius compensation of a freeform surface measurement. Measurement, 43, 469–478.

[10] Lin, Y.C., Sun, W.I. (2003). Probe radius compensated by the multicross product method in freeform surface

measurement with touch trigger probe CMM. Int. J. Adv. Manuf. Technol., 21, 902–909.

[11] Wójcik, A. (2005). The method of evaluation of mapping free form surface accuracy in reverse engieering

system. Dissertation, Cracow University of Technology.

[12] Woźniak, A., Mayer, R., Bałaziński, M. (2009). Stylus tip envelop method: corrected measured point

determination in high definition coordinate metrology. Int. J. Adv. Manuf. Technol., 42, 505–514.

[13] Woźniak, A., Mayer, R. (2012). Robust method for probe tip radius correction in coordinate metrology.

Meas. Sci. Technol., 23(2).

[14] Park, J.J., Kwon, K., Cho, N. (2006).Development of a coordinate measuring machine (CMM) touch probe

using a multi-axis force sensor. Meas. Sci. Technol., 17, 2380–2386.

[15] Savio, E., De Chiffre, L., Schmitt, R. (2007). Metrology of freeform shaped parts. Annals of the CIRP, 56/2,

810–835.


_____________________________________________________________________________________________________________________________________________________________________________________



Index 330930, ISSN 0860-8229


SINGLE-FRAME ATTITUDE DETERMINATION METHODS

FOR NANOSATELLITES

Demet Cilden Guler, Ece S. Conguroglu, Chingiz Hajiyev

Istanbul Technical University, Faculty of Aeronautics and Astronautics, 34469, Maslak, Istanbul, Turkey ( [email protected], +90 543 740 0405, [email protected], [email protected])

Abstract

Single-frame methods of determining the attitude of a nanosatellite are compared in this study. The methods

selected for comparison are: Single Value Decomposition (SVD), q method, Quaternion ESTimator (QUEST),

Fast Optimal Attitude Matrix (FOAM) − all solving optimally the Wahba’s problem, and the algebraic method using only two vector measurements. For proper comparison, two sensors are chosen for the vector observations

on-board: magnetometer and Sun sensors. Covariance results obtained as a result of using those methods have a

critical importance for a non-traditional attitude estimation approach; therefore, the variance calculations are also

presented. The examined methods are compared with respect to their root mean square (RMS) error and variance results. Also, some recommendations are given.

Keywords: attitude determination, single-frame methods, algebraic method, covariance analysis, vector

observation.


1. Introduction

The attitude determination and control subsystem of a nanosatellite is important for

maintaining a required direction of the spacecraft and its instruments. There are several methods for determining the satellite’s attitude using attitude sensors. Sun sensors and magnetometers

are very common sensors for nanosatellites because of their cost-effectiveness and commercial availability on the market with various mass and size versions. After determination of its attitude, using the actuators, a satellite should be oriented towards a specified direction. For

doing that, two or more vectors should be used as reference directions in a single-frame method which this paper is mainly focused on. Commonly used reference vectors are the Earth’s

magnetic field and unit vectors in the direction of the Sun, a known star or the centre of the Earth. Given a reference vector, the orientations of these vectors can be obtained from the measurement results of the attitude sensor.

The algebraic attitude determination methods [1−4] are based only on the vector observations. These methods are based on computing any two analytical vectors in the reference frame and measuring them in the body coordinate system [2]. The paper [3] deals with

estimating and enhancing the accuracy of an algebraic method of attitude determination. This method was examined with the use of three different vector pairs: 1) Earth’s magnetic field and

Sun vectors; 2) Earth’s magnetic field and nadir vectors; 3) Sun and nadir vectors. In order to determine the attitude accuracy, some analytical relations were found for the attitude angles

(pitch, roll and yaw). These relations include terms of the measured and theoretical vectors, used in the attitude determination. The effects of various factors on the attitude determination were examined and those which most significantly affect the accuracy were determined.

In order to increase the attitude determination accuracy, a redundant data processing algorithm,

D. Cilden Guler, E. S. Conguroglu, C. Hajiyev: SINGLE-FRAME ATTITUDE DETERMINATION METHODS …

based on the Maximum Likelihood method, was used to carry out the statistical operation on

the measurement results of three algorithms mentioned above and appropriate formulas were derived. As a result, the attitude was determined with a high accuracy in a wide range (even when the reference vectors were almost parallel). This method involves different vector pairs,

therefore it may require redundant hardware and a substantial computational load. The vectors obtained from selected sensor data and the developed models can be used in

solving the Wahba’s problem [2, 5]. Coordinate systems used as the reference frame and the body frame can be transformed to each other with necessary input parameters. The system uses single-frame methods: SVD, q, QUEST and FOAM to minimize the Wahba’s loss function and

to determine the attitude of the satellite. They are different from the algebraic method, because they use an unlimited number of direction vectors and can process all of them in one attitude

determination algorithm. In [6], the algebraic and SVD methods are compared to find an optimum attitude determination method. Also, the effects of magnetometer biases are examined in the study.

Kalman filters can give more improved results than the single-frame methods. In [7], a sigma-point Kalman filter is derived using the modified Rodrigues parameters and the real

data of attitude sensors of CBERS-2 (China Brazil Earth Resources Satellite). The unscented Kalman filter algorithm is used for attitude estimation and a gyro-based model is considered for attitude propagation. The estimated attitude is very similar to the one obtained by the Euler

angles’ propagation. Single-frame methods can also be used in filtering techniques as measurement of inputs in order to estimate the satellite’s attitude with a high accuracy. Also,

the covariance analysis can be used directly in a non-traditional method which is an integrated algorithm using linear measurements. In [8, 9], a non-traditional attitude estimation scheme has been presented and it is shown that the non-traditional methods give the attitude results for

a satellite that are superior to the traditional Kalman filters, even in the eclipse period. In [10], the performance of several methods is examined regarding their computational load

and accuracy of used algorithms. Attitude determination and estimation methods are divided into two categories: those that use and those that do not use spacecraft attitude motion models

inside their algorithms. The attitude determination methods which are considered in this paper as single-frame methods do not use knowledge about the attitude motion because they find the attitude at a single moment from the sensor-model data. In that paper, the attitude determination

algorithms are characterized as ones with a low computation load in addition to a low accuracy of spacecraft attitude angles, in comparison with such attitude estimation methods as the

extended Kalman filter, which is obvious. There were examined only methods based on observation of two vectors. Also, classification of the methods (attitude determination and estimation methods) is different; thus, there only the single-frame methods are compared to find

the most robust and the fastest method in their classification. The goal of this study is to examine the errors and variances of errors for most of the vector-

observation-based satellite attitude determination methods which are single-frame methods. Also, based on this error and variance analysis, these attitude determination methods are compared.

2. Measurement models and attitude determination methods

To find the attitude of a spacecraft, minimum two vectors should be known. In order to find these vectors, many different sensors can be applied. In this study, the sensors of magnetic field

and Sun direction vectors are used because these sensors are very common for on-board use in small satellites. In this paper, the orbital parameters are calculated using the orbit propagation

from the Two Line Elements (TLE) data for the TIMED satellite. Using mathematical models, the Sun vector (SR) and the Earth’s magnetic field vector (HR) are calculated in the orbital frame

314


(see Fig. 1). A Sun sensor and a magnetometer measure those vectors in the body frame.

In order to transform data between these frames, a transformation matrix must be known. From the dynamic and kinematic equations, the Euler angles (θ is the pitch angle, ϕ is the roll angle and ψ is the yaw angle) are calculated to form this matrix. The transformation- attitude matrix

(A) can be created using the Euler angles [11]. Numerical or analytical methods can be used to solve the kinematic and dynamic equations for the spacecraft attitude propagation [12].

2.1. Measurement models

International Geomagnetic Reference Field (IGRF) 12 is a basic magnetic field model

defining 4-input variable (r, θ, φ, t) in nT, using numerical Gauss coefficients (g, h) − global

variables in the IGRF algorithm [13]. In (1), a is a magnetic reference spherical radius

a = 6371.2 km, θ is a colatitude (deg) and φ is a longitude (deg). The transformed magnetic field model in the body coordinates with added a defined noise matrix forms the measurement

model. The mathematical (Bo) and the measurement models (Bb) of the magnetic field can be written as in the (1) and (2), respectively. B indicates the magnetic field, whereas S indicates

the Sun direction vector.

1

1 0

( , , , ) ( ) [ ( )cos ( )sin ] (cos ).N n

n m m m

o n n n

n m

aB r t a g t m h t m P

rθ φ φ φ θ

+

= =

= −∇ + ×∑∑ (1)

Fig. 1. A block diagram of the Sun and Earth’s magnetic field vectors-based single-frame attitude

determination methods.

b o B

=A noise+B B . (2)

The Sun direction in the Earth Centred Inertial (ECI) frame can be modelled. The ecliptic

longitude of the Sun is eclipticλ and a linear model of the ecliptic longitude of the Sun is ε [14].

A unit Sun direction vector (ECI

S ) in the ECI frame can be obtained as in (3). Measurements

can be modelled in the (4) with transforming data into the body coordinates and adding

a defined noise matrix. The subscript notation used in the equations defines their coordinate systems as the orbital, body or ECI frames.

Orbit Propagation

from TLE Data

Sun Direction Model

Magnetic Field

Direction Vector

(IGRF 12)

Noise

Sun Sensor

Measurements

Magnetometer

Measurements

Single-Frame

Methods

-Phi, Theta, Psi

-Covariance Matrix

315


cos

s

cos

sin

in nsi

ecliptic

ECI ecliptic

ecliptic

λ

λ ε

λ ε

=

S , (3)

2b o

= A η+S S . (4)

2.2. Algebraic method

In the algebraic method, transformation-attitude matrix (A) is determined by the observations

of two vectors. u and v are any vectors which define an orthogonal coordinate system. In this

study u and v are chosen as the Sun direction (S) and magnetic field (B) vectors.

The equations can be defined as follows [15]:

ˆ ˆ,q u= (5)

ˆ ˆ

ˆ ,ˆ ˆ

u v

r

u v

×

=

×

(6)

ˆ ˆ .s q xr= (7)

A reference matrix MR can be calculated using two reference vectors in the orbital

coordinates, ˆR

u and ˆ .Rv

[ ]ˆ ˆ ˆ .R R R R

M q r s= ⋮ ⋮ (8)

A body matrix MB can be calculated using two measured vectors in the spacecraft body

coordinates, ˆB

u and ˆ .Bv

[ ]ˆ ˆ ˆ .B B B B

M q r s= ⋮ ⋮ (9)

An attitude matrix is calculated as:

,R B

AM M=1.

B RA M M

−

= (10)

To calculate the attitude covariance matrix [1] which is in the Euler form, first the Cartesian attitude covariance matrix (Pθθ) must be known.

( ) ( )( )2 2 2 2

1 2 1 12

1[ . ],

T T T

B B B B B B B B

B B

P I u u u v u v v u

u vθθσ σ σ σ= + − + +

×

(11)

where 2

1σ is a variance of the magnetometer;

2

2σ is a variance of the Sun sensor and I is a unit

matrix with a dimension of 3 × 3. The attitude covariance matrix is a set of Euler angles:

,

TP BP Bφφ θθ= (12)

where 1B

− :

3

1

1

1,

2

k

k

k j i

AB A

φ

−

=

∂= × ∂ ∑ (13)

jφ are the Euler angles (ϕ, θ, ψ), respectively [1] .

2.3. SVD method

In 1965, Wahba defined a problem which aims to minimize the loss (L(A)) between chosen reference and measured unit vectors [5]. In the (14), bi (a set of unit vectors in the body frame)

316


and ri (a set of unit vectors in the reference frame) with their ai (a non-negative weight) are the

loss function variables obtained for instant time intervals.

21

( ) | b Ar | ,2

i i i

i

L A a= −∑ (14)

*

,

T

i i iB abr=∑ (15)

*

0( ) ( ).

TL A tr ABλ= − (16)

To simplify the loss function, *B matrix can be defined. The (16) shows that the trace of the

product of transformation matrix A and transposition of the defined matrix *B in (15) should be

maximized using statistical methods. In this study, the Singular Value Decomposition (SVD) Method is chosen to minimize the loss function problem as the optimal statistical method [16, 17].

11 22 3

*

3U VT Udiag VTB ∑ = ∑ ∑ ∑= , (17)

[1 1 det( )det( )] .T

optA Udiag U V V= (18)

The matrices U and V are orthogonal left and right matrices, respectively, and the primary

singular values (11 22 33, ,∑ ∑ ∑ ) obey the inequalities

11 22 330∑ ≥ ∑ ≥ ∑ ≥ . To find the rotation

angles of the satellite, a transformation matrix should be found from the (18) first with the

determinant of one.

A rotation angle error covariance matrix (SVDP ) is necessary for determining the instant time

intervals which give higher error results than desired.

1 1 1

2 3 3 1 1 2[(s s ) (s s ) (s s ) ] ,

T

SVDP Udiag U− − −

= + + + (19)

where the secondary singular values are 1 11 2 22 3 33

, , det(U)det(V)s s s= Σ = Σ = Σ . The

satellite has only two sensors (e.g. Sun and magnetic field sensors), thus the SVD-method fails

when the satellite is in eclipse and when two observations are parallel with the same trend of the absolute error results.

2.4. q method

In (14), a Wahba’s loss function has been defined. The attitude matrix can be parameterized with quaternions. Davenport suggested a useful solution with a unit quaternion denoted q

[16, 18]:

4

,

qq

q

=

(20)

[ ]22

4 4( ) (q ) I 2q q 2 ,T

v v v vA q q q q= − + − × (21)

*(AB ) .T Ttr q Kq= (22)

Because of the quaternion definition by the Euler theorem, there will be a rotation of the axis

and the angle. The quadratic function from (21) includes scalar and vector quaternion elements. If K is defined as a traceless matrix, the eigenvector corresponding to the maximum eigenvalue

is the optimum quaternion vector qopt in (26).

*

( ),

( )T

S Itr B zK

z tr B

− ≡

(23)

317


* *

,

TS B B≡ + (24)

* *

23 32

*

31 13

* *

12 21

,

i i i

i

B B

z B B ab r

B B

−

≡ − = × −

∑ (25)

maksimum.

opt optKq qλ≡ (26)

There is only one problem: if the eigenvectors are equal, then the correct solution cannot be obtained. Markley stated in [19] that it is not a problem of the q method, since in this situation the available data are not suitable to determine attitude (2010). The expected results in this

situation are, like the results with a Sun sensor in the eclipse, going to infinity. The q method is used in various projects and studies [16, 20] .

The rotation angle error covariance matrix can be found from the (19). A covariance goes to infinity if the eigenvectors are equal. Also, if the attitude cannot be observed then the covariance would be infinite, too.

2.5. QUEST method

The QUEST method as one of the single-frame methods aims to minimize the Wahba’s loss function in (14). Iterative techniques can be used to solve the characteristic equation in the q

method. Additionally, some assumptions can be made to obtain the solutions faster. QUEST is one of methods that uses numerical iterative techniques. In this paper, QUEST is using the

Newton Raphson method as an iterative approach with a Gibbs vector. However, with the Gibbs vector a singularity problem is associated that studies like [21] are working on to remove. The q and QUEST methods use only quaternions to obtain the attitude, but the SVD method can

solve the Wahba’s problem with Euler angles directly besides using quaternions. An advantage to the method can be brought by comparing both results obtained in the same conditions.

2 2) ( ),*

max(trB tr adjSα λ≡ − + (27)

,

*

maxtrBβ λ≡ − (28)

( ) ( ) ,

* *

max maxdet I S det StrB trBγ αλ λ ≡ − = −+ + (29)

( )2 ,I S Sα β≡ + +x z (30)

2 2

1

optq .

γγ

=

+

x

| x | (31)

To find max

,imum

λ from the ( ) 0max

det K Iλ− = characteristic equation, a defined0

λ can be used as

the initial value for simplicity [16]. The parameters are the same as in the q method.

Also, from the reference [19], the covariance matrix can be obtained as follows:

( )1

.

TiQUEST i iiaP I bb

−

= − ∑ (32)

The covariance matrix ( QUESTP ) is a result that can be used as the initial value for filtering

approaches like EKF, UKF or variance values for the whole mission period. Besides, instantaneous time intervals when the algorithm should be switched to another one can be found

out by the covariance analysis.

318


2.6. FOAM method

The loss function in (14) can be also minimized using the FOAM method [22]. First of all, the Frobenius norm should be defined in (33) using the G symbol. From this definition, the

optimal attitude matrix can be determined (35):

( )2 2

,

T

i, jFi, j

G G tr GG= =∑ (33)

( )221

2,

max FBκ λ= − (34)

( ) ( ) ( )1 2

,

T T

opt max maxFA det B B B adj B BB Bκλ κ λ

− = − + + − (35)

( )T

max opttr A B .λ = (36)

Using the FOAM method, the optimal attitude matrix can be found, and from that

a quaternion or Euler angle representation can be used. The covariance Matrix (PFOAM):

( ) ( )1

T

FOAM maxP I BBdet B κκλ

−

= +− . (37)

The matrix B defined in (17) is directly used in (37) to find the error covariance.

3. Simulation results

The simulations were performed in order to estimate the attitude of the satellite and compare

the methods to find the optimum one. The simulations were based on the orbital parameters of TIMED satellite. The algorithm was run for almost one orbital period (6000 seconds) with 1 second sampling time of the sensors. Direction cosines of standard deviations for the

magnetometer and Sun sensors were taken as 0.008 and 0.002, respectively. The attitude angle

errors found by using single-frame methods are presented in Figs. 3−7. In Fig. 2, the angles between the vector observations coming from the sensors and the pitch angle propagation can be seen in the respective frames. The angles between the vectors are close neither to 0 degree nor 180 degrees; therefore, they are not parallel to each other and will not affect the attitude

of the satellite by being not observable vectors. On the other hand, the pitch angle is closing up to 90 degrees (at about 1000th sec and 3800th sec) which causes oscillations because of the

trigonometric calculations in the methods, especially in the algebraic method.

Fig. 2. From top to bottom: An angle between measurement vectors and a pitch angle.

0 1000 2000 3000 4000 5000 6000140

145

150

155

Ang

le (

de

g)

Angle between Magnetometer and Sun Sensor Vectors

0 1000 2000 3000 4000 5000 6000-50

0

50

100

θ (

de

g)

time (sec)

319


In Figs. 3−7, the absolute attitude errors obtained by using the algebraic, SVD, q, QUEST and FOAM methods are presented. All three axes as frames in the figures can be seen as the

roll, pitch and yaw angles, respectively. Inside the dotted lines the eclipse period is defined as

a 1000−1500 second time interval. In Fig. 3, the attitude of the satellite found by the algebraic

method can be seen − with a variance propagation given in deg2 units − in the bottom frame. It should be kept in mind that single-frame methods are not capable to find accurate results for

the eclipse period because of no data are available from the Sun sensor.

Fig. 3. The attitude error and variance results obtained by the algebraic method.

Fig. 4. The attitude error and variance results obtained by the SVD method.

In Fig. 4, the SVD method with its attitude and variance results is presented in four frames.

The variance is having the same trend with the error of attitude angles as it can be seen from the graphs. In Fig. 5, attitude angles determined by the q method can also be seen. The variance

can be calculated using the same equation as with the SVD method, (19). After those methods with higher robustness, variance changes in time of the QUEST algorithm are presented

0 1000 2000 3000 4000 5000 6000

-100

0

100

φ (

deg)

Errors in Algebraic Method

0 1000 2000 3000 4000 5000 6000

-100

0

100

θ (

deg)

0 1000 2000 3000 4000 5000 6000

-100

0

100

ψ (

deg

)

0 1000 2000 3000 4000 5000 60000

0.005

0.01

time (sec)

Varia

nce (

deg2)

No

Data

0 1000 2000 3000 4000 5000 6000

-100

0

100

Errors in SVD Method

φ (

deg

)

0 1000 2000 3000 4000 5000 6000-200

0

200

θ (

de

g)

0 1000 2000 3000 4000 5000 6000-200

0

200

ψ (

de

g)

0 1000 2000 3000 4000 5000 60000

0.5

1

Vari

ance

(d

eg2)

time (sec)

320


in Fig. 6. Here, QUEST is not able to follow the trend of the error as the error covariance values.

Lastly, the absolute attitude errors and variances found by the FOAM method are shown in Fig. 7. The results of FOAM have some gaps in their propagation even if the algorithm uses measurements at a single moment, and there are some jumps in the determined attitude.

Fig. 5. The attitude error and variance results obtained by the q method.

Fig. 6. The attitude error and variance results obtained by the QUEST method.

Both magnetometer and Sun sensors are assumed to be calibrated before running the

algorithm. The Root Mean Square (RMS) error results for different time intervals are presented in Table 1 for each method. Therefore, it is possible to recognize the most reliable method for

single-frame attitude determination.

In Table 1, the 2nd, 5th, 8th, 11th, and 14th rows (Error 1) represent the interval of 0−1000

sec. The eclipse period can be seen as Error 2 within the 1000−1500 sec interval. The last rows of all methods, denoted Error 3, concern the period between 1500 sec and 6000 sec which is outside of the eclipse. Those three ranges have been selected in order to separate the periods before, during and after the eclipse period which is a crucial time interval for nanosatellites

0 1000 2000 3000 4000 5000 6000

-100

0

100

Errors in q Method

φ (

de

g)

0 1000 2000 3000 4000 5000 6000

-100

0

100

θ (

de

g)

0 1000 2000 3000 4000 5000 6000

-100

0

100

ψ (

de

g)

time (sec)

0 1000 2000 3000 4000 5000 6000

-100

0

100

Errors in QUEST Method

φ (

de

g)

0 1000 2000 3000 4000 5000 6000

-100

0

100

θ (

de

g)

0 1000 2000 3000 4000 5000 6000

-100

0

100

ψ (

de

g)

0 1000 2000 3000 4000 5000 60000

0.5

1

Vari

ance

(d

eg2)

time (sec)

321


having Sun sensors. Here, as seen from the table, the SVD and q methods are the most reliable

ones regarding robustness. If the computational burden is concerned, then the QUEST or algebraic method can possibly be selected as the base method to determine the attitude of a satellite.

Fig. 7. The attitude error and variance results obtained by the FOAM method.

Table 1. The RMS results for attitude angles obtained with different single-frame methods.

RMS Error (deg)

Roll Pitch Yaw

Algebraic Method

Error 1 5,53 1,81 5,42

Error 2 nd nd nd

Error 3 4,07 1,70 1,14

SVD Method

Error 1 3,38 1,79 0,96

Error 2 100,09 28,33 200,10

Error 3 2,69 1,64 1,07

Q Method

Error 1 3,38 1,79 0,97

Error 2 100,19 30,09 194,19

Error 3 2,69 1,65 1,07

QUEST Method

Error 1 3,39 1,87 0,98

Error 2 93,19 30,12 194,21

Error 3 2,72 1,65 1,11

FOAM Method

Error 1 4,26 2,21 1,00

Error 2 nd nd nd

Error 3 2,93 0,84 1,98

4. Conclusions

The Single Value Decomposition (SVD), q, Quaternion Estimator (QUEST), Fast Optimal Attitude Matrix (FOAM) and algebraic methods can determine the attitude with using two

0 1000 2000 3000 4000 5000 6000

-100

0

100

Errors in FOAM Method

φ (

de

g)

0 1000 2000 3000 4000 5000 6000

-100

0

100

θ (

de

g)

0 1000 2000 3000 4000 5000 6000

-100

0

100

ψ (

de

g)

0 1000 2000 3000 4000 5000 60000

0.5

1

Vari

ance

(d

eg2)

time (sec)

322


vector observations. The orbit propagation of a satellite is achieved by using chosen satellite’s

orbital parameters for 1 period of the mission. In this study, magnetometer and Sun sensors are selected as attitude sensors because of their common usage on nanosatellites. According to the simulation results, the optimal attitude results can be obtained by using the SVD or q methods.

However, the suggested methods may fail in the process of finding the desired solutions in some situations. Neither methods can estimate the attitude angles if at least one of the sensors cannot

send any measurement data. Moreover, if the Sun direction and magnetic field vectors are parallel to each other, both algorithms would also fail. In the paper there is demonstrated that the SVD gives more accurate and robust results and the QUEST is the fastest of the other

methods. Filtering methods such as the extended Kalman filter or unscented Kalman filter can be used

after those coarse attitude determination methods, to improve the results with an integration. Also, the variance information becomes an important issue to make the filter naturally adapt to the measurement results by direct using the attitude error covariance values.

Acknowledgements

The work was supported by TUBITAK (The Scientific and Technological Research Council of Turkey), Grant 113E595.

References

[1] Shuster, M.D., Oh, S.D. (1981). Three-Axis Attitude Determination from Vector Observations. Journal

of Guidance and Control., 4(1), 70−77.

[2] Wertz, J.R. (1978). Spacecraft Attitude Determination and Control. Kluwer Academic Publishers.

[3] Hajiyev, C., Bahar, M. (2002). Increase of accuracy of the small satellite attitude determination using

redundancy techniques. Acta Astronautica., 50(11), 673−679.

[4] Shuster, M.D. (2004). Deterministic Three-Axis Attitude Determination. Journal of Astronaut Sci., 52(3),

405−419.

[5] Wahba, G. (1965). Problem 65-1: A Least Squares Estimate of Satellite Attitude. Siam Review., 7(3), 409.

[6] Cilden, D., Conguroglu, E.S., Hajiyev, C. (2015). Covariance Analysis of Three-Axis Attitude Determination

Using Two Vector Measurements. 7th International Conference on Recent Advances in Space Technologies-

RAST, Istanbul, Turkey.

[7] Garcia, R.V., Matos, N.D.F.O., Kuga, H.K., Zanardi, M.C. (2015). Unscented Kalman filter for spacecraft

attitude estimation using modified Rodrigues parameters and real data. Comp. Appl. Math., 1−12.

[8] Cilden, D., Hajiyev, C., Soken, H.E. (2015). Attitude and Attitude Rate Estimation for a Nanosatellite Using

SVD and UKF. Recent Advances in Space Technologies, Istanbul, Turkey.

[9] Hajiyev, C., Cilden, D. (2016). Nontraditional Approach to Satellite Attitude Estimation. International

Journal of Control Systems and Robotics., (1), 19−28.

[10] Habib, T.M.A. (2013). A comparative study of spacecraft attitude determination and estimation algorithms

(a cost–benefit approach). Aerospace Science and Technology., 26(1), 211−215.

[11] Pasicane, V.L., Moore, R.C. (1994). Fundamentals of Space Systems. Oxford University Press, New York.

[12] Zanardi, M.C., Orlando, V., Motta, G.B., Pelosi, T., Silva, W.R. (2016). Numerical and analytical approach

for the spin-stabilized satellite attitude propagation. Comp. Appl. Math., 1−13.

[13] Finlay, C., Maus, S., Beggan, C.D., Bondar, T.N., Chambodut, A., Chernova, T.A., et al. (2010).

International Geomagnetic Reference Field: the eleventh generation. Commerce USDo.

[14] Vallado, D.A. (2001). Fundamentals of Astrodynamics and Applications. Springer Science & Business

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[15] Wertz, J.R. (1978). Spacecraft Attitude Determination and Control. Kluwer Academic Publishers, 424−425.

[16] Markley, F.L., Mortari, D. (2000). Quaternion attitude estimation using vector observations. Journal of the

Astronautical Sciences., 48(2), 359−380.

[17] Vinther, K., Jensen, K.F., Larsen, J.A., Wisniewski, R. (2011). Inexpensive Cubesat Attitude Estimation

Using Quaternions And Unscented Kalman Filtering. Automatic Control in Aerospace., 4.

[18] Shuster, M.D. (1993). A Survey of Attitude Representations. The Journal of the Astronautical Sciences.,

41(4).

[19] Markley, F.L. (1991). Attitude Determination And Parameter-Estimation Using Vector Observations −

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_____________________________________________________________________________________________________________________________________________________________________________________



Index 330930, ISSN 0860-8229


METROLOGICAL ASPECTS OF SURFACE TOPOGRAPHIES PRODUCED BY DIFFERENT MACHINING OPERATIONS REGARDING THEIR POTENTIAL FUNCTIONALITY Krzysztof Żak, Wit Grzesik Opole University of Technology, Faculty of Mechanical Engineering, Mikolajczyka 5, 45-271 Opole, Poland ( [email protected], +48 77 449 8462, [email protected])

Abstract

This paper presents a comprehensive methodology for measuring and characterizing the surface topographies

on machined steel parts produced by precision machining operations. The performed case studies concern a wide

spectrum of topographic features of surfaces with different geometrical structures but the same values of the

arithmetic mean height Sa. The tested machining operations included hard turning operations performed with CBN

tools, grinding operations with Al2O3 ceramic and CBN wheels and superfinish using ceramic stones. As a result,

several characteristic surface textures with the Sa roughness parameter value of about 0.2 µm were thoroughly

characterized and compared regarding their potential functional capabilities. Apart from the standard 2D and 3D

roughness parameters, the fractal, motif and frequency parameters were taken in the consideration.

Keywords: surface metrology, surface topography, surface roughness, areal parameters, machining operations.


1. Introduction

The visible progress in surface metrology enables the surface features generated by modern manufacturing processes to be characterized with a higher accuracy using, apart from standardized 2D roughness parameters, a number of the areal field (3D) parameters. In general,

they are defined as sets of S-parameters and V-parameters [1, 2]. This metrological challenge

concerns a big group of machine parts with an increased hardness of 45−60 HRC produced by

precision (Rz = 2.5−4 µm) and high-precision (Rz < 1µm) machining operations using super-hard (mainly PCBN) cutting tools. These advanced machining processes have been an alternative to grinding for three decades [3, 4] due to their high flexibility, possible complete machining, smaller ecological impact and higher material removal rate (MRR) [5, 6]. However,

grinding offers essential advantages in higher part dimensional accuracy and achievable higher productivity in comparison with alternative machining processes. Conventional grinding using

ceramic wheels is unable to meet the production requirements concerning hardened steels. Thus, grinding with super abrasive (CBN and PCD) wheels becomes the optimum solution,

especially in automotive industry. The discussion platform concerning the economically and technologically motivated

replacement of grinding by cutting with superhard cutting tools also focuses on the capabilities

of produced profiles against the functionality of the machined surfaces [7]. This is because cutting and abrasive processes generate different surface structures which influence distinctly

their functional properties such as resistance to abrasive wear, fluid retention ability and fatigue and contact strength [8]. Earlier concepts presented in [7] include only 2D height and amplitude parameters and the bearing area curves (BACs). Moreover, it has been observed that produced

surface topographies are not geometrically similar, although the Ra or Rz roughness parameters

K. Żak, W. Grzesik: METROLOGICAL ASPECTS OF SURFACE TOPOGRAPHIES …

are nearly of the same values. This implies the necessity of performing more extended and

advanced measurements. The first characterization and comparison of surface textures produced by turning and

grinding operations on hardened steel parts using a set of 3D roughness parameters is presented

in [9]. The 2D and 3D comparison, more oriented towards bearing area parameters, related to precision cutting and abrasive operations, is provided in [10]. The objective of this study is a

comprehensive characterization and comparison of the surface textures of representative hard turned, and differently ground and honed surfaces using a number of standardized 3D roughness parameters as well as the fractal dimension, motif and frequency parameters. This wide

spectrum of measurement techniques seems to be adequate for the description of complex textures produced by random machining processes.

2. Machining tests and measurements of surface roughness

Cylindrical samples made of a 41Cr4 hardened (57 ± 1 HRC) steel with an initial roughness

average value of Sa = 0.42 µm were differently finished by turning, grinding and superfinishing

in order to reduce the Sa parameter value to about 0.2 µm. The machine tools were an Okuma Genos L200E-M CNC lathe and a conventional

cylindrical grinding machine. The machining conditions are as follows: 1. Hard turning (HT) using a CBN TNGA 160408 S01030 chamfered insert, vc = 150 m/min,

f = 0.06 mm/rev, ap = 0.15 mm. 2. Cylindrical grinding using an electro-corundum (Al2O3) (GR-CW), a 350 × 25 × 127 32A

grinding wheel, vc = 11.9 m/s, ae = 0.025 mm, fa = 3.5 mm/rev. 3. Cylindrical grinding using an INTER DIAMENT B107 K100 SV grinding wheel (GR-

CBNW), vc = 36 m/s, ae = 0.025 mm, fa = 1.6 mm/rev.

4. External honing (super-finish) SF using a 99A320N10V ceramic stone, an oscillation frequency of 680 osc/min and an amplitude of 3.5 mm, an applied force of 40 N, a cooling

and lubrication medium − 85% kerosene and 15% machine oil.

Surface topographies generated by selected machining operations were recorded using a 3D

contact profilometer with a diamond stylus radius of 2 ± 0.5 µm. The scanning process was

performed on small, 250 µm × 250 µm square shape surfaces in order to generate 201 different

surface profiles by the diamond stylus. The measurement resolution along X and Z axes

obtained with an inductive transducer for roughness measurements is equal to 0.001 µm. The measuring signals were filtered using a Gaussian digital filter. The raw data were automatically

inserted into a Digital Surf, Mountains Map package in order to determine both 2D and 3D

roughness parameters and perform 3D visualization of the machined surfaces. In consequence, the representative values of surface roughness were determined as the average values from each

of 201 sets of measurements performed on individual profiles. The obtained surface topographies were described based on the following four groups of

parameters: a) standardized 2D and 3D surface roughness parameters: height, amplitude,

horizontal, hybrid and functional defined in the ISO 25178 standard [2, 11]; b) fractal dimension; c) standardized motif parameters and d) frequency spectra characteristics.

3. Experimental results and discussion

3.1. Characterization of surface topographies

Representative surface topographies obtained in hard turning (HT) and abrasive (both GR and SF) operations are visualized in Figs. 1a to 1d. Regarding the surface quality criterion these

326


operations can be classified as precision machining, because the maximum roughness height

Rz < 2 µm [10].

a) Sa = 0.21µm, Sz = 1.56 µm

b) Sa = 0.21 µm, Sz = 3.86 µm

c) Sa = 0.22 µm, Sz = 2.87µm

d) Sa = 0.20 µm, Sz = 2.59 µm

Fig. 1. Surface textures produced by HT (a); ground using Al2O3 (b); CBN wheel (c) and honed (d).

The measured Sa values range between 0.20 and 0.22 µm. As specified in Fig. 1, Sz

parameter increases from 1.56 µm for hard turning to 3.86 µm for grinding with Al2O3 wheel, which evidently suggests different surface functionality.

a) Sal = 0.07 mm, isotropy: 6.74%

b) Sal = 0.01 mm, isotropy: 3.88%

c) Sal = 0.02 mm, isotropy: 5.38%

d) Sal = 0.02 mm, isotropy: 1.99%

Fig. 2. Representative autocorrelation functions for turned (a); ground (b, c) and honed (d) surfaces.

327


The autocorrelation function (ACF) enables to distinguish the isotropic content from mixed

isotropic-anisotropic surfaces which represent typical machined surfaces. As shown in Fig. 2, all machined surfaces have a strong anisotropy. This is because the autocorrelation has a central lobe which extends along one direction. The turned and honed surfaces are periodic-anisotropic

(Figs. 2a and 2d) because they have other maxima which indicate the periodicity of these surfaces. The ground surfaces are mixed, between anisotropic and random structures (Figs. 2b

and 2c) because the ACF represents one central lobe. The values of the fastest decay autocorrelation length (Sal) are equal to 0.07 for hard turned and 0.01 or 0.02 for abrasive treated surfaces, respectively. A larger value of Sal = 0.07 for the turned surface denotes that it

is dominated by low spatial frequency components (see Fig. 12a). Dynamic influences of the machining system are reproduced along the lays and, as a result, the “central lobe” of the ACF

decays faster in the direction parallel to the periodicity of the lay.

3.2. Characterization of function related parameters

Figure 3 presents shapes of 3D BACs and associated ADF curves obtained for the compared

machining operations. In particular, hard turning (1) produces surfaces with a positive skew

Ssk = 0.24 but finish grinding (2 and 3) generates surfaces with a negative skew Ssk − (−0.31)

for GR-CW versus (−0.48) for GR-CBNW. Moreover, Fig. 3b suggests that hard turning and grinding produced topographies with diametrically different ADF shapes which result in

various bearing and contact properties. The superior bearing properties (Ssk = −0.69) were obtained when sharp irregularities produced by hard turning were removed by abrasive stone during additional honing (BAC #4 in Fig. 3a). Additionally, values of the areal material ratio

Smr(c), the inverse areal material ratio Sdc(mr) and the peak extreme height Sxp are given in Fig. 3a.

a) 1. Sdc = 0.66 µm, Sxp = 0.44 µm, 2. Sdc = 1.97 µm,

Sxp = 0.60 µm, 3. Sdc = 1.13 µm, Sxp = 0.65µm, 4. Sdc

= 0.46 µm, Sxp = 0.61 µm

b) 1. Ssk = 0.24, Sku = 2.56, 2. Ssk = −0.31, Sku = 5.41,

3. Ssk = −0.48, Sku = 3.70, 4. Ssk = −0.69, Sku = 3.03

Fig. 3. 3D BAC shapes (a) and ADF distributions (b) for turned (1); ground (2 and 3) and honed (4) surfaces;

the initial hard-turned surface (5).

Additional information on the fluid retention can be obtained using a technique of vectorisation of micro-valleys’ network (Fig. 4) available in the used Mountain Map package

[12] generated on the machined surface. The maximum depth of valleys is between 1 and 2 µm

and their width is predominantly equal to 0.5 µm. Additionally, the average density of valleys is between 500 and 700 cm/cm2, respectively. This comparison indicates that abrasive

operations produce surfaces with a greater number of deeper valleys (Fig. 4b). These data coincide well with the distributions of the volume functional parameter (Vmp and Vvv) shown in Fig. 5. The functional analysis of 3D BACs is based on four volume parameters, including:

0

20

40

60

80

100

0 20 40 60 80 100

Cu

t l

ev

el

c

Smr (c), %

(1) HT

(2) GR-CW

(3) GR-CBNW

(4) SF

(5) INIT

100 %

57.9 %

48.9 %

60.5 %

1

3

2

82.4 %4

5

74.5 %

0

3

6

9

12

15

18

21

0 5 10 15 20 25 30 35

(1) HT

(2) GR-CW

(3) GR-CBNW

(4) SF

(5) INIT

1

2

3

4

5

328


the peak material volume (Vmp), the core material volume (Vmc), the core void volume (Vvc)

and the valley void volume (Vvv) ones. [1, 2]. Their values obtained for HT and abrasive operations are as follows (in order HT/GR-CW/GR-CBNW/SF): Vmp = 0.0125/ 0.0150/

0.0112/0.0063 µm3/µm2; Vmc = 0.254/0.225/0.247/0.252 µm3/µm2; Vvc = 0.342/0.292/

0.310/0.255 µm3/µm2; Vvv = 0.0213/0.0383/0.0403/0.0353 µm3/µm2. For instance, higher

values of Vvv = 0.0383 and 0.0403 µm3/µm2 suggest better fluid retention ability of ground

surfaces (for a turned surface Vvv = 0.0213 µm3/µm2).

a) HT

1.07 µm/0.50 µm/523 cm/cm2

b) GR-CRW

1.98 µm/0.46µm/709 cm/cm2

c) GR- CBNW

1.76 µm/0.46µm/708 cm/cm2

d) SF

1.61 µm/0.34µm/663 cm/cm2

Fig. 4. Vectorised micro-valley networks for turned (a); ground with Al2O3 wheel (b); ground with CBN wheel

(c) and honed (d) surfaces. Three values give the average depth, width and density of micro-valleys.

a)

b)

Fig. 5. Functional volumetric parameters for different finishing operations: distribution of volume parameters

for hard turning (a); distributions for all machining operations (b).

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

HT GR-CW GR-CBNW SF

Vo

lum

e f

un

cti

on

al

pa

ram

ete

rs

, µ

m3/µ

m2

Vmp

Vmc

Vvc

Vvv

329


The comparison of function-related parameters [2] is given in Figs. 6 and 7. In these case

studies three areal (V) material ratio parameters − the reduced core (Sk), peak (Spk) and valley

(Svk) height (Fig. 6) and their ratios − Spk/Sk, Svk/Sk, Spk/Svk (Fig. 7) were used in order to assess the nature of specific surface textures. In particular, the ratio of Spk/Sk may be helpful to

distinguish between two surfaces with indistinguishable roughness average Sa [11].

a)

b)

Fig. 6. Areal bearing area parameters for different finishing operations: distribution for hard turning (a);

distributions for all machining processes (b).

It can be seen in Fig. 6b that all cutting and abrasive operations generated surfaces with

comparable values of the reduced core height between 0.6−0.7 µm. On the other hand, visible differences between the reduced peak (Spk) height and reduced valley (Svk) height can be

observed in Fig. 6b. Moreover, both ground surfaces with the same Sa have vastly different Spk/Sk values

of 0.426 and 0.282 (Fig. 7a). They are further reduced to 0.145 by honing. As shown in Fig. 7b, the ratio of Spk/Sk correlates well also with the Vmp volume parameter, whereas the ratio

of Svk/Sk with the Vvc volume parameter and micro-valleys density. Additional relationships can be observed (Fig. 7a) between the ratio of Spk/Svk and Sdc and Sxp material ratio parameters.

a)

b)

Fig. 7. Functional relationships between selected 3D V-parameters.

3.3. Characterization of spatial and hybrid parameters

The set of 3D parameters includes four spatial parameters, three of which are texture

parameters. The ground and − especially − honed surfaces contain distinctly more summits

within the scanned area − Sds = 2006.1 1/mm2 (SF) versus 1440.7 1/mm2 (HT). The comparable

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

HT GR-CW GR-CBNW SF

Be

ar

ing

pa

ra

me

ter

s, µ

m

Sk

Spk

Svk

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

HT GR-CW GR-CBNW SF

Ma

ter

ial

ra

tio

pa

ram

ete

rs

,

µm

He

igh

t p

ara

me

ter

s, µ

m

Spk/Sk

Svk/Sk

Spk/Svk

Sdc (20)

Sxp

0

100

200

300

400

500

600

700

800

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

HT GR-CW GR-CBNW SF

Mic

ro-v

all

ey

s d

en

sit

y,

cm

/c

m2

Fu

nc

tio

na

l v

olu

me

pa

ram

ete

rs

, µm

3/µ

m2

Vmp

Vvv

M-VD

330


small texture aspect ratio Str = 0.02−0.07 for all machined surfaces indicates stronger directionality (anisotropy) but its values for both cutting and abrasive operations, which are less

than 0.1, are characteristic for highly anisotropic surfaces [13]. The texture direction Std close to 90º for all three surfaces indicates that the dominant surface lay is perpendicular to the measurement direction. The values of Sal parameter are given in Fig. 2.

The values of three 3D hybrid parameters emphasize additional geometrical differences in the compared textures. Higher slopes Sdq of about 6º were obtained for ground surfaces versus

3° for turned and honed surfaces. The values of average summit curvature Ssc of about 0.007

µm−1 for the turned and honed surface and about 0.02 µm−1 for the ground surfaces are typical

for machined surfaces (0.004−0.03 µm−1 given in [13]). The Sdr parameter (the developed interfacial area ratio) of 0.16% is higher for the ground surfaces (Fig. 1b and c) than for the

turned and honed surface (Figs. 1a and 1 d) − 0.04%/0.03%.

3.4. Motifs and fractals

The motif analysis is performed on an unfiltered surface profile divided into a series

of windows [13, 14], as shown for all machining variants in Fig. 8. In this study the mean depth of roughness motif R, the mean spacing of roughness motif AR and the largest motif height Rx

were analysed.

a)

b)

c)

d)

Fig. 8. Examples of the motif graphs for hard turned (a); ground with Al2O3 wheel (b);

ground with CBN wheel (c) and honed (d) surfaces.

R = 0.618 µm AR = 0.0994 mm Rx = 1.37 µm Pt = 1.47 µm

0 0.5 1 1.5 2 2.5 mm

µm

-2

-1

0

1

2


0 0.5 1 1.5 2 2.5 mm

µm

-2

-1

0

1

2


0 0.5 1 1.5 2 2.5 mm

µm

-2

-1

0

1

2


0 0.5 1 1.5 2 2.5 mm

µm

-1

-0.5

0

0.5

331


Fig. 9. Functional relationships between Sz(Rz) and Rx(R) motif parameters.

The ground surfaces include distinctly deeper pits (Rx = 1.68 and 2.55 µm) in comparison

with the hard-turned and honed surfaces (Rx = 1.37/1.18 µm), which is in accordance with the volume bearing parameters (Fig. 5). Fig. 9 shows that the Rx motif parameter is stronger correlated with the Sz parameter than with the Rz one, although motifs are based on the 2D

analysis. On the other hand, the R motif parameter of 0.6−0.7 µm seems to be independent of the used machining operations and coincides with the Rz changes.

a)

b)

Sfd: HT-2.37, GR-CW-2.41, GR-CBN-2.42, SF-2.52;

Sds: HT-1441 1/mm2, GR-CW-1605 1/mm2, GR-CBNW- 1885 1/mm2, SF-2006 1/mm2.

Fig. 10. Functional relationships between selected 3D S-parameters and the fractal dimension.

The fractal dimension concept enables a description of the complexity of engineering

surfaces in the form of a single number. The fractal dimension may vary between the theoretical limits of 1 for a straight line and 2 for a space-filling curve. It should be noted that real machined surfaces are called multifractal because obviously they are formed by several different

processes, each with its characteristic topographical features [14]. Digital Surf, Mountains Map software [15] enables to calculate the fractal dimension for a surface profile or real surface

by means of a method of enclosing boxes or morphological envelopes. In the method of enclosing boxes in real units, applied in this study, the fractal dimension is determined by

calculating the slope of regression line which corresponds best to the lnN versus lnε plot (where

N is the number of boxes and ε is the size of a box). The values of 3D fractal dimension Sfd determined by means of the method of enclosing

boxes are equal to 2.37, 2.41/2.42 and 2.52 for turned, ground and honed surfaces. On the other

hand, the values of 2D fractal dimension D determined from the surface profiles are equal to 1.08, 1.56/1.61 and 1.66, respectively.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0

0.5

1

1.5

2

2.5

3

3.5

HT GR-CW GR-CBNW SF

Su

rfa

ce

pa

ra

me

ter

s, µ

m

Mo

tif

pa

ra

me

ter

s, µ

m

R

Rx

Sz

Rz

1400

1500

1600

1700

1800

1900

2000

2100

2.25

2.3

2.35

2.4

2.45

2.5

2.55

HT GR-CW GR-CBNW SF

De

ns

ity

of

su

mm

its,

pe

ak

s/

mm

2

Fra

cta

l d

ime

nsi

on

of

the

surf

ace

Sfd

Sds

0

2

4

6

8

10

12

14

16

18

20

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

HT GR-CW GR-CBNW SF

Ar

ith

me

tic

me

an

su

mm

it

cu

rv

atu

re o

f th

e s

ur

fac

e,

pe

ak

s/m

m

Au

to-c

or

rela

tio

n l

en

gth

, mm

Sal

Ssc

332


The functional relationships between fractal dimension Sfd and Sal, Ssc and Sds spatial and

hybrid parameters are revealed in Fig. 10. It can be noticed in Fig. 10a that the Sfd is strongly correlated with the density of summits (Sds) and Sfd = 2.52 corresponds with the maximum

value of Sds = 2006 1/mm2 determined for the honed surface. For this function (Sfd = 5 × 10 −

7Sds − 0.0015(Sds) 2 + 3.4693) the R-square is equal to 0.8363. In addition, it correlates with the arithmetic summit curvature (Ssc) and the autocorrelation length Sal parameter which

characterize the texture anisotropy (Figs. 2 and 10b).

3.5. Frequency analysis

The characteristic PSD spectra obtained for hard turned, ground and honed surfaces are

presented in Fig. 11. The PSD is very sensitive to all disturbances of the generated surfaces appearing in the machining system.

a) Amplitude: A-0.0895µm; B-0.184µm, Wavelength: A-0.060 mm; B-

0.416 mm

b) Amplitude: A-0.0829µm; B-0.0772µm; C-0.0826µm; D-0.074µm, Wavelength: A-0.155 mm; B-0.168 mm; C-0.201 mm; D-0.358 mm

c) Amplitude: A-0.068 µm, B-0.074 µm, C-0.063µm, D-0.105 µm;

Wavelength: A-0.148 mm, B-0.185 mm, C-0.223 mm, D-0.316 mm

d) Amplitude: A-0.205µm, Wavelength: A-0.100 mm

Fig. 11. The averaged power spectral density for turned (a); ground with Al2O3 wheel (b); ground with CBN

wheel (c) and honed (d) surfaces.

333


It is evident from Fig. 11a that the PSD spectrum contains only one low-frequency

component with the same wavelength as the feed rate of 0.06 mm (60 µm) and the amplitude

of 0.09 µm. On the other hand (Figs. 11b and 11c), the ground surfaces contain several

components with longer wavelengths but distinctly lower amplitudes of 0.04−0.07 µm than the

hard-turned surfaces. In particular, very small amplitudes of about 0.07 µm were recorded for the surfaces produced by grinding using a CBN wheel (Fig. 11c). On the other hand, the highest

amplitude of about 0.2 µm appeared during the honing operation which was performed on

a conventional lathe.

4. Conclusions

1. Distinct changes of topographical features of machined surfaces produced by different

cutting and abrasive processes are revealed using both standardized and non-standardized measuring techniques. According to the engineering knowledge this enables to generate

surfaces with desired functional properties, for instance with required bearing or locking properties, resistance to abrasive wear, fluid retention capability, fatigue and contact strength, depending on their engineering applications.

2. Precision grinding and super-finish operations cause that successively more material is concentrated in the vicinity of surface peaks. For these cases the ADF function has

a symmetrical shape with a large kurtosis and/or a large skew. 3. Comparing surface topographies using the autocorrelation operator indicates their strong

anisotropy and the necessity of 3D measurement. 4. 3D bearing area curves and appropriate functional parameters suggest, according to [13],

that the ground hard surfaces have enhanced fluid retention abilities. This is due to a large

negative Ssk value and higher Vvv volumes for ground textures. 5. The hard turned and CBN-ground textures have comparable Vmp and Spk parameter values

and similar tribological properties. According to the engineering practice demonstrated in [12] and [13] the best tribological performance of the honed surface is due to minimum Vmp and Spk values.

6. The fractal dimension Sdf correlates well with the density of summits. Because a higher value of the Sdf parameter denotes a large surface area (a larger Sdr parameter), a possible

consequence should be that in such a case the normal contact pressure decreases and the wear rate decreases with increasing the Sdf value.

7. The PSD charts enable directly to recognize a possible influence of the machining system

stability on the surface texture and, as a result, also to eliminate inconvenient machining conditions causing excessive vibrations.

List of abbreviations

GR − grinding

HT − hard turning

SF − super finishing

S-parameters − Surface-parameters

V-parameters – Volume-parameters

ACF − autocorrelation function

ADF − amplitude density function

BAC − bearing area (material ratio) curve

CBN − cubic boron nitride

MRR – machining removal rate

334


PCD − polycrystalline diamond

PSD − power spectral density AACF – autocorrelation function

GR-CW − grinding (GR) using conventional wheel (CW)

GR-CBNW − grinding (GR) using CBN wheel (CBNW)

HT/GR-CW − hard turning/grinding using conventional wheel sequential process HT/ GR-CBNW – hard turning/ grinding using CBN wheel sequential process

References

[1] Jiang, X.Jm, Whitehouse, D.J. (2012). Technological shifts in surface metrology. CIRP Annals-Manuf.

Technol., 61(2), 815−836.

[2] Leach, R. (ed.) (2013). Characterization of areal surface texture. Berlin, Springer-Verlag.

[3] Grzesik, W. (2008). Advanced machining processes of metallic materials. Elsevier, Amsterdam.

[4] Klocke, F. (2011). Manufacturing processes 1. Cutting, Berlin, Springer.

[5] König, W., Berktold, A., Koch, K.F. (1993). Turning versus grinding- a comparison of surface integrity

aspects and attainable accuracies. CIRP Annals-Manuf. Technol., 42(1), 39−43.

[6] Davim, J.P. (ed.) (2011). Machining of hard materials. London, Springer.

[7] Klocke, F., Brinksmeier, E., Weinert, K. (2005). Capability profile of hard cutting and grinding processes.

CIRP Annals-Manuf. Technol., 54(2), 557−580.

[8] Grzesik, W., (2016). Prediction of the functional performance of machined components based on surface

topography: a survey. J. Mater. Eng. Perf., 25(10), 4460−4468.

[9] Waikar, R.A., Guo, Y.B. (2008). A comprehensive characterization of 3D surface topography induced by

hard turning versus grinding. J. Mat. Proc. Technol., 197, 189−199.

[10] Grzesik, W., Rech, J., Wanat, T. (2007). Surface finish on hardened bearing steel parts produced by superhard

and abrasive tools. Int. J. Mach. Tools and Manuf., 47, 255−262.

[11] ISO 25178, part 2 (2012), Geometrical product specification (GPS)− surface texture: areal. Terms, definitions and surface texture parameters, ISO.

[12] Digital Surf, Mountains Map software, www. digitalsurf.com.

[13] Griffiths, B. (2001). Manufacturing surface technology. Surface integrity and functional performance.

London, Penton Press.

[14] Dietzsch, M., Papenfuss, K., Hartman, T. (1998). The MOTIF-method (ISO 12085)- a suitable description

for functional, manufactural and metrological requirements. Int. J. Mach. Tools and Manuf., 38, 625−632.

[15] Thomas, T.R., (1999). Rough Surfaces. London, Imperial College Press.


_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Oct. 14, 2016; accepted on Jan. 21, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0030.


Index 330930, ISSN 0860-8229


RAPID DESIGN OPTIMIZATION OF MULTI-BAND ANTENNAS BY MEANS

OF RESPONSE FEATURES

Sławomir Kozieł, Adrian Bekasiewicz

Reykjavik University, School of Science and Engineering, Menntavegur 1, 101 Reykjavik, Iceland ([email protected], [email protected], +354 599 6886)

Abstract

This work examines the reduced-cost design optimization of dual- and multi-band antennas. The primary challenge is independent yet simultaneous control of the antenna responses at two or more frequency bands. In order to

handle this task, a feature-based optimization approach is adopted where the design objectives are formulated on

the basis of the coordinates of so-called characteristic points (or response features) of the antenna response. Due to

only slightly nonlinear dependence of the feature points on antenna geometry parameters, optimization can be

attained at a low computational cost. Our approach is demonstrated using two antenna structures with the optimum

designs obtained in just a few dozen of EM simulations of the respective structure.

Keywords: antenna design, antenna measurements, computer-aided design, surrogate modelling, feature-based

optimization.


1. Introduction

Contemporary antenna engineering heavily relies on full-wave electromagnetic (EM) analysis. EM solvers offer accurate performance analysis, as well as account for interactions

of the structure with environmental components (e.g. connectors, housing) [1, 2]. However, EM simulations tend to be expensive, especially for complex structures, so that their use in automated design, e.g. parametric optimization, may be impractical [3]. EM-driven design becomes even

more challenging in the case of multi-objective design (e.g. antenna size vs. electrical performance) [4, 5] or in the case of dual- and multi-band antennas, where requirements on the

reflection response have to be satisfied for several frequency bands of interest [6, 7]. Traditional methods involving parameter sweeps become problematic in such cases, especially for compact antennas with considerable EM cross-couplings, that make independent control of frequency

bands difficult [8]. Computationally efficient EM-driven design of antennas can be achieved by means

of surrogate-based optimization (SBO) methods [9, 10]. SBO involving physics-based surrogates are particularly promising due to combining the speed of the underlying low-fidelity

model and reasonable accuracy obtained by applying suitable correction techniques. The low-fidelity models are typically obtained from coarse-discretization EM simulations. The popular methods for surrogate construction include space mapping [10], frequency scaling [10], shape-

preserving response prediction [11], adaptive response correction [12], manifold mapping [13], and adaptively adjusted design specifications [14]. Combining physics-based modelling with

data-driven modelling may also produce promising results [1, 5]. In terms of conventional optimization methods, only gradient-based search seems to ensure comparable efficiency if derivative data are obtained through cheap adjoint sensitivities [15, 16].

Recently, feature-based optimization (FBO) has been proposed for the design of microwave filters [17], where the original design problem is reformulated in a so-called feature space,

S. Koziel, A. Bekasiewicz: RAPID DESIGN OPTIMIZATION OF MULTI-BAND …

leading to a less nonlinear functional landscape to be optimized compared with the original

formulation (typically, w.r.t. S-parameters versus frequency). This work is based on our original conference publication of [18], where FBO concept has been adopted for the design of dual-band antennas. Here, we reformulate the considered framework to allow for optimization

of multi-band structures.". We demonstrate that reformulating the antenna design task with the use of suitably defined features leads to considerable simplifications, so that the optimization

process can be accomplished at a much lower computational cost compared with that of conventional algorithms. Two application examples are provided. Numerical results are supported by experimental verification of the fabricated antenna prototypes.

2. Feature-based optimization for multi-band antennas

The purpose of this section is to formulate a feature-based optimization algorithm for multi-

band antenna design. There are several challenges that need to be addressed, such as highly nonlinear responses, multiple objectives (in particular, independent control of several operating

frequencies), but also a large number of adjustable geometry parameters of the antenna at hand.

2.1. Response features of dual-band antennas

Figure 1 shows typical responses of a dual-band antenna and, more importantly, their changes

resulting from modification of the antenna geometry (the responses correspond to the example considered in Section 3.1). The responses are evaluated along a selected line segment in the design

space defined as y(t) = t⋅y1 + (1 – t)⋅y2, where 0 ≤ t ≤ 1, whereas y1 and y2 are the two reference

designs. High nonlinearity and considerable variability of the responses can be observed. Fig. 2 shows changes of the response features, here selected as the minima of the reflection responses (i.e. the points corresponding to the antenna resonances) and the point corresponding to –10 dB

reflection levels. Each point is described by its two coordinates (frequency and level). Note that, despite of a high nonlinearity of the reflection response, the behavior of the feature points is close

to linear. Consequently, expressing the design goals based on the feature points and using feature-based surrogates, the optimization process is expected to be considerably speeded up .

2.2. Antenna design in feature space

The original design problem (in S-parameter vs. frequency domain) is formulated as: * argmin ( ( ))=

x

x R xU , (1)

where U is an objective function defined with the EM model response, i.e. S11 versus frequency.

Fig. 1. A family of dual-band responses corresponding to their geometries along a certain line segment in the design

space showing highly nonlinear dependence of the reflection characteristic on the geometry variables

of the structure.

3 3.5 4 4.5 5 5.5 6-25

-20

-15

-10

-5

0

Frequency [GHz]

|S11|

338


Given several operating frequencies fk, k = 1, …, Nf, for a multi-band antenna, a typical

formulation would be to minimize max |S11(x)| at f1, …, |S11(x)| at fNf in respect to x (in particular to ensure that the reflection is less than –10 dB at all frequencies). Another option could be to maximize the antenna bandwidth around the operating frequencies. In any case, in

(1) one needs to directly handle highly nonlinear responses, as shown in Fig. 1. Here, the design task is reformulated based on the feature vectors F(x) and L(x) (i.e.

frequency and level coordinates of the respective feature points), as follows:

* argmin ( ( ), ( ))=

x

x F x L xF

U , (2)

where UF is an appropriate objective function. The major advantage of this formulation is that the functional landscape of the problem (2) is much less nonlinear than that for the original

problem (1). Also, because of handling the frequencies of the feature points, it is possible to easily control the frequency location of the resonances, which is difficult in (1).

If the goal is to minimize antenna reflection at the operating frequencies fk , the function UF

uses only Nf feature points [f(1)(x) l(1)(x)], …, [f(Nf)(x) l(Nf)(x)] corresponding to the reflection response minima, and is defined as follows:

2(1)

1

( )(1)

( )

( )

( ) max ( ),..., ( )

( )

β

= + −

x

x x x

x

⋮ ⋮f

ff

N

F

N

N

ff

U l l

ff

. (3)

It can be observed that, according to (3), the main objective is to minimize antenna reflection.

On the other hand, the penalty term enables to control the operating frequencies of the structure.

It should be noted that the values of the coefficient β should be sufficiently large to ensure that the contribution of the penalty term is comparable to the primary objective for an unacceptably

large frequency allocation error (we use β = 100).

Fig. 2. The feature points (the reflection minima and the points corresponding to –10 dB levels),

as described in Section II.1, corresponding to antenna geometries along the same line segment

parameterized by t as in Fig. 1.

0 0.5 1

3.4

3.6

3.8

t

Fre

q.

[GH

z]

0 0.5 1

-16

-14

t

|S11|

[dB

]

0 0.5 1

5.3

5.35

5.4

t

Fre

q.

[GH

z]

0 0.5 1

-30

-25

-20

-15

t

| S11|

[dB

]

0 0.5 1

3.4

3.6

3.8

t

Fre

q.

[GH

z]

0 0.5 1-12

-10

-8

t

|S11|

[dB

]

0 0.5 1

3.5

3.6

3.7

3.8

3.9

t

Fre

q.

[GH

z]

0 0.5 1-12

-10

-8

t

| S11|

[dB

]

0 0.5 1

5.24

5.26

5.28

5.3

5.32

t

Fre

q.

[GH

z]

0 0.5 1-12

-10

-8

t

|S11|

[dB

]

0 0.5 1

5.35

5.4

5.45

t

Fre

q.

[GH

z]

0 0.5 1-12

-10

-8

t

| S11|

[dB

]

339


2.3. Optimization algorithm The problem (2) is solved iteratively as:

( ) ( )

( 1) ( ) ( )

|| ||arg min ( ( ), ( ))+

− ≤

=

x x

x F x L xi i

i i i

F S Sr

U , (4)

where x(i), i = 0, 1, …, is a sequence approximating x*, whereas FS(i) and LS

(i) are linear approximation models of the feature point vectors F(x) and L(x) determined in the current design x(i). Finite differentiation is used to establish the models with n perturbed designs around

x(i), i.e., x(i) + hk, k = 1, …, n, where hk = [0 … 0 dk 0 … 0]T, dk > 0 [19], and the corresponding feature points F(x(i) + hk), L(x(i) + hk) are extracted from the respective antenna responses. We

have:

( ) ( )

1 1

( ) ( ) ( )

( ) ( )

[ ( ) ( )] /

( ) ( ) ... ( )

[ ( ) ( )] /

+ −

= + ⋅ − + −

F x h F x

F x F x x x

F x h F x

Ti i T

i i i

S

i i T

n n

d

d

, (5)

( ) ( )

1 1

( ) ( ) ( )

( ) ( )

[ ( ) ( )] /

( ) ( ) ... ( )

[ ( ) ( )] /

+ −

= + ⋅ − + −

L x h L x

L x L x x x

L x h L x

Ti i T

i i i

S

i i T

n n

d

d

. (6)

The algorithm (4) is embedded in a trust-region framework with the search radius r(i) updated using standard rules [19].

3. Verification examples

In this section, the considered feature-based method for fast design of multi-band antennas is verified. Two design examples are considered: a dual-band patch antenna with 8 design variables and a triple-band uniplanar dipole with 10 adjustable parameters. For the latter

structure, the numerical results are supported with measurements of the fabricated antenna prototypes.

3.1. Dual-band patch antenna

Our first example is concerned with verification of a dual-band planar antenna shown in Fig. 3 [20]. The structure consists of two radiating elements in the form of a quasi-micro-strip patch

with an inset feed and a monopole radiator, both connected in a cascade. The antenna is excited through a 50 ohm microstrip line. The lower and upper resonant frequencies are introduced by the monopole and the patch, respectively. The ground plane is trimmed below the patch

component to increase the number of degrees of freedom (hence, it is referred to as a quasi-micro-strip patch).

The antenna is constructed on a 0.762 mm thick Taconic RF-35 dielectric substrate with a relative permittivity of 3.5 and a loss tangent of 0.0018. The design variables are x = [L l1 l2 l3

W w1 w2 g]T. The parameters o = 7, w0 = 1.7, l0 = 10, and s = 0.5 are fixed. The unit for all parameters is mm. The lower and upper bounds for the parameters are l = [10 1 5 1 4 0.2 1 –4]T and u = [20 6 17 7 16 4 6 6]T, respectively. Note that negative g results in trimming ground

plane below the patch component of the radiator The EM antenna model R is implemented in CST Microwave Studio and contains

~1,900,000 hexahedral mesh cells. Its average simulation time on a dual Xeon E5540 machine with 6 GB RAM is 12 minutes.

340


Two cases were considered regarding the design requirements:

− Case I: operating frequencies 3.5 GHz and 5.3 GHz; − Case II: operating frequencies 2.4 GHz and 4.8 GHz.

In both cases, the goal is to allocate the resonances at the respective operating frequencies and

to minimize reflection at these frequencies. The initial design is xinit = [17.0 1.8 11.7 4.1 12.9 0.7 1.3 0.2]T mm. As shown in Fig. 4, this design is poor and very far from satisfying design

specifications in both considered cases. More importantly, as the reflection response is flat and close to zero in the initial design in the vicinity of the operating frequencies, local optimization would be stuck in the initial design when the original formulation of the problem is considered

(cf. (1)). This was verified using a pattern-search algorithm [21]. Consequently, global optimization methods would have to be used with an associated very high computational cost.

Figure 4 shows the antenna responses in the initial and in the final design x*I = [17.17 2.19 13.20 5.00 12.78 0.94 4.00 2.62]T mm found by FBO. Note that the design quality is very good with the resonances well centred at the operating frequencies of interest and with the reflection levels

< – 25 dB. The optimization cost was 72 evaluations of the EM model (8 algorithm iterations), which is

low, given the complexity of the problem and the fact that FBO is a derivative-free method. Local optimization working for the original formulation of the problem failed to find an acceptable design.

Figure 5 shows the results for Case II. The optimum design is x*II = [17.64 2.89 13.84 6.90

13.55 0.20 5.03 4.09]T mm, and it was obtained at the cost of 90 evaluations of the EM antenna model (10 algorithm iterations). Again, the design quality is very good with resonances centred

at the operating frequencies and the reflection minima below –30 dB. Note that the optimum design is at a considerable distance from the initial one (response-wise). If the optimization starts from x*I, a solution comparable to x*II is obtained in just four iterations.

Fig. 3. The dual-band patch antenna geometry [20]. The ground plane is marked using the lighter shade of grey.

Fig. 4. The optimization results, Case I. Antenna responses in the initial design (- - -) and in the design found

by the feature-based optimization algorithm (—).

L

l1

l2

l3

W

w1

w2

o

g

s

w0

l0

o

1 2 3 4 5 6 7-30

-20

-10

0

Frequency [GHz]

|S11| [d

B]

341


Fig. 5. The optimization results, Case II. Antenna responses in the initial design (- - -) and in the design

found by the feature-based optimization algorithm (—).

3.2. Triple-band planar dipole antenna

Our second example is a triple-band uniplanar dipole antenna shown in Fig. 6. The structure

is based on the geometry introduced in [22]. The used substrate is a 0.762 mm thick Taconic RF-35 (see Section 3.1). The antenna is constructed as a stack of three narrow, long ground

plane slits separated by two thicker, short slots. The radiator is fed through a 50 ohm coplanar waveguide (CPW). The vector of adjustable parameters is x = [l1 l2 l3 l4 l5 w1 w2 w3 w4 w5]T, whereas dimensions l0 = 30, w0 = 3, s0 = 0.15 and o = 5 remain fixed. The unit for all geometric

parameters is mm. The search space is defined using the following lower and upper bounds: l = [30 5 22 5 15 0.2 1.2 0.2 1.2 0.2]T and u = [50 15 29 15 21 2.2 4.2 2.2 4.2 2.2]T. The EM

antenna model R (~100,000 cells; simulation: 6 min) is prepared in CST Microwave Studio and simulated using its time domain solver.

Two sets of design specifications are considered:

− Case I: operating frequencies: 2.45 GHz, 3.65 GHz, and 5.77 GHz; − Case II: operating frequencies: 1.85 GHz, 2.95 GHz, and 5.15 GHz.

Similarly to Section 3.1, the goal of the optimization was to minimize the antenna reflection for the selected operating frequencies. The initial design parameters are xinit = [36 14 26 12 20

1 3 1 2 1]T mm. As it can be seen from Fig. 7, the initial design is closer to the desired specifications compared with the example discussed in Section 3.1. Consequently, for the Case I, the original formulation of the design problem given by (1) can be used to find the

desired design solution using a local search algorithm (here, the pattern-search one). However, for the Case II, the algorithm was stuck at the local minimum which was away from the desired

solution. For Case I, the comparison of the antenna responses in the initial design and in the design

optimized using the feature-based method is shown in Fig. 7. The final vector of parameters is

x*I = [39.04 14.99 28.26 12.26 18.91 1.20 1.2 0.2 1.35 0.77]T. It should be noted that the structure response is well centred at the chosen operating frequencies with the reflection levels

below –22 dB. The cost of the algorithm operation was 130 evaluations of the antenna model (12 iterations).

At the same time, the pattern-search algorithm required 278 EM simulations to obtain a similar

antenna solution. Thus, for the considered case, the numerical cost of pattern-search optimization is almost 50 percent higher than that of FBO.

For Case II, the vector of optimal parameters is: x*II = [45.28 9.48 28.99 10.63 19.29 1.45 3.55 0.62 1.68 0.43]T. The frequency characteristics of the structure in the initial and optimized design are compared in Fig. 8. Again, the antenna features good electrical performance at the

selected operating frequencies with the reflection level below –12 dB. The numerical cost of the design process is 100 evaluations of the EM antenna model (9

iterations). Having in mind noticeable distance of the first two operating frequencies from the initial design, the cost is very low.

1 2 3 4 5 6 7-30

-20

-10

0

Frequency [GHz]|S11| [d

B]

342


Fig. 6. The triple-band dipole antenna geometry with highlighted design parameters.

Fig. 7. The triple-band dipole antenna optimization results: Case I. Antenna responses in the initial design (- - -)

and in the design found by the feature-based optimization algorithm (—).

Fig. 8. The triple-band dipole antenna optimization results: Case II. Antenna responses in the initial design (- - -)

and in the design found by the feature-based optimization algorithm (—).

The results obtained for both antenna designs have been experimentally validated.

Photographs of the fabricated structures are shown in Fig. 9, whereas Fig. 10 presents comparison of their simulated and measured reflection characteristics. For Case I, the measured

lowest operating frequency is slightly shifted down by about 50 MHz. Nonetheless, the remaining bands are well aligned. For Case II (Fig. 10(b)), the measured bandwidth is slightly broader around the second operating frequency compared with the simulated one.

The difference, however, is only about 60 MHz. Generally, the results are in a good agreement. Small discrepancies between the simulated and measured responses are due to the use of a

simplified antenna EM model without an EM connector. The latter has been excluded from simulations in order to reduce the computational cost of the optimization process.

l1

l2

l3

l4

l5

w1

w2

w3

w4

w5

l0

w0

s0

1 2 3 4 5 6 7 8-25

-20

-15

-10

-5

0

Frequency [GHz]

| S11| [d

B]

1 2 3 4 5 6 7 8-25

-20

-15

-10

-5

0

Frequency [GHz]

| S11| [d

B]

343


Fig. 9. Photographs of the fabricated dipole antenna prototypes: Case I (top), and Case II (bottom).

a)

b)

Fig. 10. Comparison of the simulated (– –) and measured (––) reflection characteristics obtained

for the triple-band dipole antenna: Case I (a); and Case II (b).

4. Conclusion

Rapid and precise design optimization of dual- and multi-band antennas has been presented. The key component of the optimization procedure that ensures its computational efficiency is

reformulation of the design problem in a feature space of suitably-defined characteristic points, where the objectives are less nonlinear functions of the geometry parameters of the antenna (as compared with the original formulation, typically, in the space of S-parameters versus

frequency). This enables to yield the optimized design at a low cost corresponding to just a few dozen of EM simulations. Working examples of a dual- and triple-band antennas as well as

their experimental verification confirm validity of the proposed approach. Our further work will

1 2 3 4 5 6 7 8-25

-20

-15

-10

-5

0

Frequency [GHz]

| S11| [

dB

]

1 2 3 4 5 6 7 8-25

-20

-15

-10

-5

0

Frequency [GHz]

| S11| [d

B]

344


focus on application to the method for other multi-band microwave structures, such as filters,

couplers or power dividers.

Acknowledgement

The authors would like to thank Computer Simulation Technology AG, Darmstadt,

Germany, for making CST Microwave Studio available. This work is partially supported by the Icelandic Centre for Research (RANNIS) Grants 141272051, 163299051 and by National Science Centre of Poland Grant 2014/15/B/ST7/04683.

References

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[2] Koziel, S., Ogurtsow, S., Zieniutycz, W., Bekasiewicz, A. (2015). Design of a planar UWB dipole antenna

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[3] Lizzi, L., Viani, F., Azaro, R., Massa, A. (2007). Optimization of a spline-shaped UWB antenna by PSO.

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[4] Chamaani, S., Abrishamian, M.S., Mirtaheri, S.A. (2010). Time-domain design of UWB Vivaldi antenna

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[5] Koziel, S., Bekasiewicz, A. (2015). Fast multi-objective optimization of narrow-band antennas using RSA

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[7] Liu, Y.F., Wang, P., Qin, H. (2014). Compact ACS-fed UWB monopole antenna with extra Bluetooth band.

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[8] Wang, L., Xu, L., Chen, X., Yang, R., Han, L., Zhang, W. (2014). A compact ultrawideband diversity antenna

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[9] Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidynathan, R., Tucker, P.K. (2005). Surrogate-based

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[10] Bandler, J.W., Cheng, Q.S., Dakroury, S.A., Mohamed, A.S., Bakr, M.H., Madsen, K., Søndergaard, J.

(2004). Space mapping: the state of the art. IEEE Trans. Microwave Theory Tech., 52(1), 337−361.

[11] Koziel, S., Ogurtsov, S., Szczepanski, S. (2012). Rapid antenna design optimization using shape-preserving

response prediction. Bulletin of the Polish Academy of Sciences. Tech. Sci., 60, 143−149.

[12] Koziel, S., Bandler, J.W., Madsen, K. (2005). Towards a rigorous formulation of the space mapping

technique for engineering design. IEEE Int. Symp. Circuits Syst., 6, 5605−5608.

[13] Koziel, S., Leifsson, L., Ogurtsov, S. (2013). Reliable EM-driven microwave design optimization using

manifold mapping and adjoint sensitivity. Microwave Opt. Tech. Lett., 55, 809−813.

[14] Koziel, S., Ogurtsov, S. (2013). Rapid optimization of omnidirectional antennas using adaptively adjusted

design specifications and kriging surrogates. IET Microwaves, Ant. Prop., 7(15), 1194−1200.

[15] El Sabbagh, M.A., Bakr, M.H., Bandler, J.W. (2006). Adjoint higher order sensitivities for fast full-wave

optimization of microwave filters. IEEE Trans. Microw Theory Tech., 54, 3339−3351.

[16] Koziel, S., Bekasiewicz, A. (2015). Fast EM-driven size reduction of antenna structures by means of adjoint

sensitivities and trust regions. IEEE Ant. Wireless Prop. Lett., 14, 1681−1684

[17] Koziel, S., Bandler, J.W. (2015). Rapid yield estimation and optimization of microwave structures exploiting

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[18] Koziel, S., Bekasiewicz, A., Leifsson, L. (2016). Expedited design of dual-band antennas using feature-based

optimization. European Conf. Ant. Prop., Davos, 1−4.

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[19] Conn, A.R., Gould, N.I.M., Toint, P.L. (2000). Trust-region methods. MPS-SIAM Series on Optimization,

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Nov. 19, 2016; accepted on Jan. 14, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0025.



NOVEL VARIABLE STRUCTURE MEASUREMENT SYSTEM

WITH INTELLIGENT COMPONENTS FOR FLIGHT VEHICLES

Kai Shen1,2), Maria S. Selezneva2), Konstantin A. Neusypin2), Andrey V. Proletarsky2)

1) Nanjing University of Science and Technology, School of Mechanical Engineering, Nanjing, 210094, P.R. China ( [email protected], +8 925 373 8978) 2) Bauman Moscow State Technical University, Faculty of Computer Science and Control Systems, Moscow, 105005, Russia ([email protected], [email protected], [email protected])

Abstract

The paper presents a method of developing a variable structure measurement system with intelligent components

for flight vehicles. In order to find a distinguishing feature of a variable structure, a numerical criterion for selecting

measuring sensors is proposed by quantifying the observability of different states of the system. Based on the Peter K. Anokhin’s theory of functional systems, a mechanism of “action acceptor” is built with intelligent components,

e.g. self-organization algorithms. In this mechanism, firstly, prediction models of system states are constructed

using self-organization algorithms; secondly, the predicted and measured values are compared; thirdly, an optimal

structure of the measurement system is finally determined based on the results of comparison. According to the

results of simulation with practical data and experiments obtained during field tests, the novel developed

measurement system has the properties of high-accuracy, reliable operation and fault tolerance.

Keywords: flight vehicle, variable structure measurement system, the degree of observability, self-organization

algorithm, integrated navigation system.


1. Introduction

Vehicles that are capable of sustained motion through air and space are termed as flight vehicles (FV), and they are generally classified as aircrafts, space-crafts and rockets. All flight

vehicles require manipulation (i.e. control or adjustment) of their position, velocity and orientation for efficient completion of flight missions based upon the measurement information about operation states [1]. However, in practice the measurement information is usually

disturbed by internal and external noise. Thus, in order to improve accuracy of on-board measurement systems, a novel design scheme is developed with intelligent components based

on the Peter K. Anokhin’s functional system theory [2, 3]. As we all know, on-board measurement systems usually consist of an inertial navigation

system (INS), a global navigation satellite system (GNSS), a ground-based radio navigation

system (GRNS), a terrain-referenced navigation system (TRNS), a continuous visual navigation system (CVNS) etc. [4]. The above mentioned systems are generally integrated using

Kalman filtering [4, 5] to fuse navigation information with different characteristics. However, the operability of those sensors varies all the time with changes of external environment.

For example, when our flight vehicles are working in a battlefield environment, it may be impossible to access the position, navigation, and timing (PNT) information with ordinary GNSS receivers. Therefore, the novel measurement system presented in this paper is designed

with a variable structure. To achieve this goal, some selection criteria of measurement information, e.g. a numerical criterion of the degree of observability (DoO), must be formulated

for time-varying conditions.

K. Shen, M. S. Selezneva, et al.: NOVEL VARIABLE STRUCTURE MEASUREMENT SYSTEM …

In addition, according to the Peter K. Anokhin functional system theory, a mechanism

of “acceptor of the results of action” [2] (or just “action acceptor”) is necessary for our new developed measurement system, because it can help us to select an optimal combination of measuring sensors and to determine a better measurement structure for a current working

period. To introduce this mechanism, self-organization algorithms (SOA) [6] functioning as an intelligent component are suggested to be put into use.

The paper is organized as follows. In Section 2, a methodology of quantitative observability analysis with the degree of observability, functioning as a kind of selection criterion of measurement information, is introduced for linear time-varying (LTV) systems. In Section 3,

self-organization algorithms used for constructing prediction models are briefly examined. In Section 4, an analytical methodology for optimizing system parameters and modelling

in synthesis of a measurement system is presented. In Section 5, a novel measurement system is developed on the basis of the Peter K. Anokhin’s functional system theory. In order to clearly demonstrate performance and effectiveness of the proposed measurement system, the results

of simulation using practical data and field test results are presented.

2. Measurement selection criterion and degree of observability

In this section, we are interested in finding a figure of merit for each state-variable that can

reflect how observable the state-variable is. A criterion having this function may be termed the numerical criterion of the degree of observability. Moreover, the degree of observability can

further serve as an indicator in selecting better measuring sensors for a current working period in formulating variable structure measurement systems [1]. As we have mentioned above, the external environment and internal system states are continuously changing in time.

Therefore, the system of interest is commonly expressed as a linear time-varying system:

, 1 1 1k k k k k− − −

= +x F x w , (1)

k k k k= +z H x v , (2)

where k

x is a vector of state; 1k−

w is a vector of input noise; k

z is a vector of measurement;

kv is a vector of measurement noise;

, 1k k−F is a state transfer matrix;

kH is a measurement

matrix.

We assume that the input 1k−

w and measurement k

v noise is the white Gaussian noise, and

there is no evident correlation between them, i.e. 0T

j kE = v w for any j and k .

In respect to the system represented by (1) and (2), a measurement kz may be reformulated

as follows [7]:

1 1 1, 1 1

1 1 1, 2 1, 1 1, 2 2, 1

1 2 1,

k k k k

k k k k k k k k

k n k n k n k n k k k k n k n k n k k k

k n k n k n

+ + + + +

+ − + − + − + − + + − + − + − + +

+ − + − + −

= +

= + +

= +

+ + +

⋯ ⋯ ⋯

⋯ ⋯

⋯

z H x v

z H F x H w v

z H F F x H F F w

H w v

(3)

where n is the order of the system. Then, we can rewrite the expression (3) in a matrix form as:

* *

k k k k= +z O x v , (4)

348


where 1*

1

...

k

k

k

k n

+

+ −

=

z

z

z

z

, 1 1,

1 1, 2 1,

k

k k k

k

k n k n k n k k

+ +

+ − + − + − +

=

H

H FO

H F F

⋯

⋯

;

1 1* 1

1 1, 2 2, 1 1 2 11

...

kk

k k kk

k

k n k n k n k k k k n k n k nk n

+

+

+ ++

+

+ − + − + − + + + − + − + −+ −

+ = =

+ + +

vv

H w vvv

H F F w H w vv

⋯ ⋯ ⋯

⋯ ⋯

.

A matrix k

O is termed the local observability matrix of an LTV system [8]. To examine

the local observability over a period from k to 1k n+ − , we can use as the observability rank

criterion being the local observability matrix k

O of rank n for the period, i.e.

krank n=O . (5)

Considering (4), we can step by step obtain a relationship of state-variables and measurement as:

T T T

k k k k k k k

∗ ∗

= +O z O O x O v , (6)

or

T T T

k k k k k k k

∗ ∗

= −O O x O z O v , (7)

then

1 1

T T T T

k k k k k k k k k

− −∗ ∗ = − x O O O z O O O v , (8)

and finally

† †

k k k k k

∗ ∗

= −x O z O v , (9)

where † means the Moore-Penrose pseudoinverse of matrix.

Let †

k k k

∗

=y O z , considering (4), we can obtain a scalar form of vector k

y as:

1, 2, 1 , 1

i i i i

k k k k k n k k ny a z a z a z

+ + −= + + +⋯ , (10)

where i

ky is the i-th component of vector

ky ,

,

( 1, , )i

j ka j n= ⋯ are time-varying elements of the

i-th row in the matrix †

kO .

Correspondingly, the measurement noise * † *

k k k=ς O v in a scalar form is:

*

1, 2, 1 , 1

i i i i

k k k k k n k k na v a v a vς

+ + +

+ + −= + + +⋯ , (11)

where *i

kς is the i-th component of vector *

kς .

Furthermore, the variance of measurement noise *i

kς may be expressed as:

( ) ( ) ( )2 2 2

*

1, 2, ,

i i i i

k k k n k kR a a a R

+ = + + + ⋯ , (12)

where k

R+ is the variance of direct measurement noise

kv+ .

Therefore, the degree of observability for an LTV system can be defined as [7]:

( )

( )

2

2*

i

ki

ki i

k

E x R

DE y R

+ =

. (13)

349


From (12), we know that the ratio of the variance values of measurement noise is ( )2

,

1

,

ni

j k

j

a

=

∑

thus we can rewrite (13) and finally obtain:

( )

( ) ( )

2

22

,

1

i

i

k ni i

j k

j

E x

D

E y a=

=

∑

. (14)

In practice, ( )2

iE x

and ( )2

iE y

in (14) are usually calculated as:

( ) ( )1

2 21k n

i i

l

l k

E x xn

+ −

=

= ∑

, (15)

( ) ( )1

2 21k n

i i

l

l k

E y yn

+ −

=

= ∑. (16)

It is apparent from (14) that the system parameters in the matrix , 1k k−

F have an indirect

influence on the degree of observability by the elements ,

( 1, , )i

j ka j n= ⋯ in the pseudoinverse

matrix of observability †

kO . In practical applications, this feature makes it possible to optimize

physical model parameters and to determine optimal variable structures for measurement

systems.

3. Algorithms for constructing prediction models

In order to guarantee high-precision selection and fusion of information, the mechanism of “action acceptor” is necessary in our novel variable structure measurement systems. In this mechanism, except for the application of the degree of observability, algorithms for

constructing prediction models are also required for further comparing the a posteriori and predicted information. From the results of comparison [2, 9], an optimal structure of the

measurement system can be finally determined for the current working period in accordance with the operation conditions of flight vehicles. In this section, we shall introduce some algorithms, e.g. self-organization algorithms, for constructing mathematical prediction models.

In general, we define a mathematical prediction model as:

( )1

,

L

k i i i k

i

M a f xµ

=

=∑ , (17)

where i

µ is a basic function from the function set s

F ( ) ( ), | 1, ,s i i i k

F a f x i Lµ= = ⋯ and ia is

an amplitude, if is a frequency, L is the number of basic functions.

As the basic functions, we usually select three types of functions to build mathematical prediction models owing to the dynamic features of flight vehicles. a) A linear trend (function) has a form:

( )ˆ ,L l l

k l l k k kx a b k t d= + , (18)

where ˆLkx is a predicted value, ,

l l

k kk d are a slope and a constant of the linear function, ,

l la b

are coordinates of the reference point.

b) A nonlinear harmonic trend (function) is:

( ) ( )ˆ sin cosN s s c c

k k k k k k k k kx A t B tω ϕ ω ϕ= + + + , (19)

where ˆNkx is a predicted value, , , , , ,

s c s c

k k k k k kA B ω ω ϕ ϕ are amplitudes, frequencies and phases

of the trigonometric functions.

350


c) A Modified Demark trend is expressed as:

1 1

ˆ ˆD D

k k kx x C

− −

= + , (20)

where ˆDkx is a predicted value and

1 1 1 1 1ˆ ˆ

L L N N

k k k k kC x xζ ζ

− − − − −

= +, (21)

where 1 1,

L N

k kζ ζ

− −

are weighing factors within a range from 0 to 1.

In order to find an optimal solution j

χ for mathematical prediction models, we would like

to introduce a quadratic criterion [10] with respect to the amplitude ia as:

( ) ( )1

22 , 2 , 0

k n

j i i j i i i j

j k

f x a f xχ µ µ

+ −

=

− + = ∑ . (22)

Then, we may differentiate it by the amplitude ia and obtain:

( )

( )

1

1

2

,

,

k n

j i i j

j k

i k n

i i j

j k

f x

a

f x

χ µ

µ

+ −

=

+ −

=

=

∑

∑. (23)

With (23) we can easily find a good optimal solution of prediction models based on the self-organization selection criteria [6]:

a) the minimum deviation criterion:

( )2

2 1

2

1

ˆ ˆ

min,

LP Q

i i

i

M L

i

i

x x

z

=

=

−

∆ = →

∑

∑ (24)

where ˆPix and ˆQ

ix designate two parts of a predicted value,

iz is a measurement value.

b) the regularity criterion:

( )2

2 1

2

1

ˆ

min

L

i i

i

R L

i

i

z x

z

=

=

−

∆ = →

∑

∑, (25)

where ˆix is a predicted value.

Based on the above-mentioned basic functions (18) ‒ (20), we can thus build some self-

organization algorithms by utilizing the self-organization selection criteria (24) and (25). One of the most effective algorithms is a so-called self-organization algorithm with redundant

trends, as shown in Fig. 1, where SC are selection criteria, C are competitive prediction models.

Fig. 1. A functional scheme of self-organization algorithm with redundant trends.

351


Similarly, evolutionary algorithms, e.g. genetic algorithms and neural networks, can also

function as tools for building prediction models. Eventually, we can obtain an optimal mathematical prediction model using the above proposed algorithms.

4. Analytical methodology for optimizing system parameters and modelling

On the basis of the concept of measurement system synthesis [1, 9], it is necessary to rationally reduce the number of model parameters of the system. For this purpose, we would like to introduce a practical methodology for optimizing system parameters in accordance with

the external and internal changes. In the practical implementation of parameter optimization, we can simply divide the system

parameters into three types considering the changing rates of parameter values. For example, all the system parameters are classified as “slow”, “normal” and “fast” variables. Correspondingly, during processing the measurement information in practice, we may make

some modifications, as follows: slow changing parameters are replaced with constants; fast changing parameters are replaced with their average values. Next, according to the problem

statement, the clarification (or correction) of variables is made. As a result, an hierarchy diagram of optimizing system parameters considering their changing rates is formulated, as shown in Fig. 2.

Fig. 2. An hierarchy diagram of optimizing system parameters considering their changing rates.

The presented hierarchy method of optimizing system parameters can be applied in the

mechanism of “action acceptor” to building measurement systems with intelligent components. In respect to the modelling optimization with optimizing parameters, based on the theory

of system synthesis [9], a novel practical methodology for modelling is developed by adopting the numerical criteria of the degree of observability and the criteria of self-organization selection. A functional diagram of modelling in measurement systems with intelligent

components is presented in Fig. 3.

352


Fig. 3. A functional diagram of modelling in measurement systems with intelligent components.

In Fig. 3, dominant parameters are selected using the criterion of the degree of observability

with a low threshold. Furthermore, different types of models are formulated depending on the operation modes of flight vehicles. However, it should be noted that for intensive manoeuvring

modes a high threshold value of the degree of observability is further suggested to be used to guarantee effective information processing and high accuracy of parameter determination.

In this section, we examine the analytical methodology for optimizing system parameters and modelling, and illustrate practical techniques by their functional diagrams. According to the above proposed design concepts, the novel developed measurement system structure is

guaranteed to be compact, which is beneficial in practical applications.

5. Variable structure measurement system with intelligent components

Rapid development of cybernetics, computer engineering, biotechnology and artificial intelligence leads to the appearance of measurement systems with intelligent components. Based on the systematic synthesis concept and the Peter K. Anokhin’s functional system theory

[1, 3], in this section we present a new type of measurement system with a variable structure and show its working principles as well as practical advantages.

As we all know, the operation environments (external and internal) of flight vehicles are constantly changing. Thus, a variable structure of the measurement system should be designed to adapt to those changes. In order to do that, the degree of observability must be used as an automatic selection criterion (or indicator) of measurement information. Except for that, the mechanism of “action acceptor”, consisting of a block of information fusion and selection

(BIFS), an algorithm for constructing models (ACM) and a block of prediction algorithms (BPA), also needs to be formulated.

Based on the above-mentioned numerical criterion of the degree of observability, self-organization algorithms and other practical methodologies, a novel variable structure measurement system with intelligent components has been developed, as shown in Fig. 4, where

Sensor 1 is the basic navigation sensor (e.g. an inertial navigation system), Sensors 2 ‒ N are external supporting navigation systems (e.g. GNSS, TRNS, CVNS, and so on) [4, 11, 12], BEA

is a block of estimation algorithms (e.g. Kalman filtering [5, 13]), θ is actual navigation

353


information, x is a navigation error, z is measurement information, x is an estimate, ˆx is

a predicted value, xɶ is an estimation error.

Fig. 4. A functional scheme of a novel variable structure measurement system with intelligent components.

In the block of information fusion and selection, the optimal structure of measurement

system is determined by comparing the measured and predicted information on the basis of the

degree of observability. With the changes of external and internal conditions, the structure of measurement systems is always in the process of change. Therefore, this process is similar

to an intelligent decision-making procedure and thus guarantees the optimization of the system structure.

In order to comprehensively explain the working principles of the proposed novel measurement system, we carried out simulations with the use of practical data. To measure the position and velocity of our flight vehicles, we used GNSS receivers, TRNS and CVNS

cameras. Accordingly, the degrees of observability of velocity errors obtained by using different measuring sensors were calculated, as shown in Fig. 5.

Fig. 5. The degrees of observability of navigation errors obtained by different sensors.

Figure 5 clearly shows the variant trend and the percentage of having the degree

of observability for different navigation sensors. The results are advantageous in calculation of information-sharing factors during the information fusion [13, 14]. In addition, the calculated

354


degree of observability can serve as an indicator in selection of better external supporting

navigation systems for a current working period. On the basis of the above results, it is easy to decide which of the supporting sensors should

be selected during a current period and how to change or optimize the structure of the measurement system in order to adapt to the changes of internal states and external conditions.

Moreover, the field tests were also carried out in a semi-real environment. During the tests, we set a change period of the measurement structure equal to 20 seconds taking into account the practical requirement and on-board computation capability. The test results are shown in Fig. 6.

Fig. 6. The field test results of the novel developed variable structure measurement system.

As shown in Fig. 6, based on analysis of the observability, a combination of basic INS and

supporting TRNS worked with a better accuracy than that of other measurement functional structures in an interval from 640 to 660 sec. Thus, in order to obtain an optimal measurement

structure, TRNS was selected as the external supporting navigation system. Similarly, in the next intervals CVNS and GNSS were successively selected. According to the results of simulation and experiments, the novel developed measurement system is characterized by

high accuracy, self-adaption and fault tolerance. In the novel developed measurement system, we set INS as the basic navigation system,

because it has the advantages of strong autonomy, instantaneous navigation parameters and good concealment, which lead to the all-weather global operation of the system. During functioning of the novel developed measurement system, we always select only one external

supporting sensor to combine with the INS in each time interval, which can guarantee strong anti-interference capability (e.g. anti-electromagnetic interference in battlefield environments)

of the whole measurement system.

6. Conclusions

The paper presents a method of developing a variable structure measurement system with

intelligent components. In order to achieve this goal, a numerical criterion of the degree of observability and algorithms for constructing prediction algorithms (e.g. modified self-organization algorithms) are proposed. On the basis of the Peter K. Anokhin’s functional system

theory, a novel measurement system with a variable structure is developed for improving accuracy of the system and adapting it to changes of environment. The new proposed

measurement system has an intelligent decision-making capability and guarantees continuous

640 650 660 670 680 690 700

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time (s)

Na

vig

atio

n E

rro

r (m

/s)

CVNS

TRNS

Reference

GNSS

Selected TRNS

Selected CVNS

Selected GNSS

355


optimization of the system structure. According to the results of simulation with the use

of practical data as well as the results of field tests, the novel developed measurement system is characterized by high accuracy, self-adaption, strong anti-interference capability and fault tolerance.

Acknowledgement

This research was supported by the Programme of Introducing Talents of Discipline to Universities in P.R. China (“111 program” No. B 16025) and the Russian Foundation for Basic

Research (Project No. 16-8-00522).

References

[1] Selezneva, M.S., Neusypin, K.A. (2016). Development of a measurement complex with intelligent

component. Measurement Techniques, 59(9), 916–922.

[2] Anokhin, P.K. (1974). Biology and neurophysiology of the conditioned reflex and its role in adaptive

behavior. Pergamon Press, 190–254.

[3] Proletarsky, A.V., Shen, K., Neusypin, K.A. (2015). Intelligent control systems: Contemporary problems in theory and implementation in practice. 2015 5th International Workshop on Computer Science and

Engineering: Information Processing and Control Engineering, Apr. 15–17, Moscow, 39–47.

[4] Groves, P.D. (2013). Principles of GNSS, inertial, and multisensor integrated navigation systems. Artech House, Inc., Boston, MA, USA, 419–448.

[5] Mirosław, Ś., Magdalena, D. (2015). Application of Kalman filter in navigation process of automated guided vehicles. Metrol. Meas. Syst., 22(3), 443–454.

[6] Neusypin, K.A., Proletarsky, A.V., Shen, K., et al. (2014). Aircraft self-organization algorithm with redundant trend. Journal of Nanjing University of Science and Technology, 5, 602–607.

[7] Shen, K., Neusypin, K.A., Proletarsky, A.V. (2014). On state estimation of dynamic systems by applying scalar estimation algorithms. Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control

Conference, Aug. 8–10, Yantai, China, 124–129.

[8] Chen, Z. (1991). Local observability and its application to multiple measurement estimation. IEEE

Transactions on Industrial Electronics, 38(6), 491‒496.

[9] Proletarsky, A.V., Nikiforov, V.M., Neusypin, K.A. (2014). Certain aspects of designing the control complex of an advanced spacecraft. Systemy I Pribory Upravleniia, 1, 5‒11.

[10] Shen, K., Proletarsky, A.V., Neusypin, K.A. (2016). Algorithms of constructing models for compensating navigation systems of unmanned aerial vehicles. 2016 International Conference on Robotics and Automation

Engineering, Aug. 27–29, Jeju-Do, South Korea, 104‒108.

[11] Groves, P.D., Handley, R.J., Runnalls, A.R. (2006). Optimising the integration of terrain-referenced navigation with INS and GPS. Journal of Navigation, 59 (1), 71‒89.

[12] Won, D.H., Lee, E., Heo, M., Sung, S. Lee, J., Lee, Y.J. (2014). GNSS integration with vision-based navigation for low GNSS visibility conditions. GPS Solutions, 18(2), 177‒187.

[13] Carlson, N.A. (1990). Federated square root filter for decentralized parallel processors. IEEE Transactions

on Aerospace and Electronic Systems, 26(3), 517‒525.

[14] Xing, Z.R., Xia, Y.Q. (2016). Distributed federated Kalman filter fusion over multi-sensor unreliable networked systems. IEEE Transactions on Circuits and Systems, 63(10), 1714‒1725.


_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Dec. 01, 2016; accepted on Jan. 14, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0024.



MODELLING OF INFLUENCE OF HYPERSONIC CONDITIONS

ON GYROSCOPIC INERTIAL NAVIGATION SENSOR SUSPENSION

Igor Korobiichuk1), Volodimir Karachun2), Viktorij Mel’nick2), Maciej Kachniarz3)

1) Warsaw University of Technology, Faculty of Mechatronics, Św. A. Boboli 8, 02-525, Warsaw, Poland ( [email protected], +48 22 234 8506) 2) National Technical University of Ukraine, Kyiv Polytechnic Institute, 37 Peremogy, Kyiv, Ukraine ([email protected], [email protected]) 3) Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, Poland ([email protected])

Abstract

The upcoming hypersonic technologies pose a difficult task for air navigation systems. The article presents

a designed model of elastic interaction of penetrating acoustic radiation with flat isotropic suspension elements

of an inertial navigation sensor in the operational conditions of hypersonic flight. It has been shown that the

acoustic transparency effect in the form of a spatial-frequency resonance becomes possible with simultaneous

manifestation of the wave coincidence condition in the acoustic field and equality of the natural oscillation

frequency of a finite-size plate and a forced oscillation frequency of an infinite plate. The effect can lead to

additional measurement errors of the navigation system. Using the model, the worst and best case suspension

oscillation frequencies can be determined, which will help during the design of a navigation system.

Keywords: hypersonic technologies, gimbals, oscillation modes, acoustic transparency, navigation system.


1. Introduction

Today, ships are armed with 100−145 mm calibre automatic cannons which have not only limited range but also insufficient shooting accuracy in a modern combat. Therefore, the main range of possible targets is acquired by missiles, which are very expensive and, besides, have

considerable dimensions. To solve this problem, the United States Navy plans by 2025 to supply a rail gun capable of destroying any targets with cheap projectiles and at long ranges. The electromagnetic rail gun is developed by BAE SYSTEMS and GENERAL ATOMICS (Fig. 1). The testing is scheduled to take place on board of the newest high-speed vessel JHSV

Millinocket. Moreover, the developers of railguns offer to equip also usual powder cannons with

hypersonic projectiles, which would dramatically improve their ability to hit any targets,

including airborne ones. Rail guns can project at a speed of 5M at a distance of 400 km. According to the military

forecasts, such guns can hit any target. According to the Department for Development of Marine Systems of NAVSEA NAVY, the rail gun features are planned to be partly implemented in

traditional powder cannons. It means, that an HVR hypersonic projectile is planned to be developed in two major United States Navy calibres: 155 mm and 127 mm. Thus, a universal core would serve for two types of both powder cannon and rail gun. Naturally, when firing from

a powder cannon, the HVR speed would be lower than when firing from a rail gun. The difference would be 3 M and 5 M, respectively. Nevertheless, the speed will be twice higher

than while using gunpowder. An HVR projectile should become an alternative to expensive

I. Korobiichuk, V. Karachun, et al.: MODELLING OF INFLUENCE OF HYPERSONIC CONDITIONS …

anti-aircraft missiles and 155 mm LRLAP projectiles which cost $ 400,000 per unit for Zumwalt class destroyers.

Fig. 1. A hypersonic projectile of a rail gun can replace expensive missiles.

However, advantages that create new means of fire support give rise to a lot of air navigation

problems. They consist in high temperatures, extreme vibration, shock N-wave and penetrating acoustic radiation. Diffuse sound fields would fundamentally change the dynamics of on-board equipment mechanical systems’ features and affect the performance characteristics of avionic instruments in general, such as inertial navigation systems.

Two-stage gyroscopic instruments are widely used as sensitive elements of gyroscopically stabilized platforms and inertial navigation systems. Therefore, the requirement of high precision indications is crucial for accurate building of reference directions on mobile objects. This applies primarily to the launch vehicles (LV) and hypersonic aircraft, the propulsion systems of which create a high sound pressure (up to 180 dB) in a rather broad frequency range. This will also apply to hypersonic projectiles, since the existing solid-state and MEMS systems are not accurate and simultaneously robust enough for such applications.

The main feature of penetrating radiation impact is its spatial nature. On the one hand, traditional means of combating external perturbations are ineffective, and, on the other hand, there is a need of a fundamentally new approach to design diagrams, namely a change from lumped parameter systems to distributed parameter systems. Let us demonstrate how this is applied to gimbals’ flat fragments.

The goal of the research is to evaluate the risk of manifestation of local resonance peculiarities in gimbals when using an aircraft.

In order to achieve the aim, the following tasks should be accomplished: 1. Building a design diagram of the studied phenomenon. 2. Choosing a method of building a mathematical model with which particularities of resonance

type would have been obvious and visible for further analysis when studying the dynamics of gimbals in general, especially to evaluate additional errors of autonomous positioning.

3. Evaluating feasibility and effectiveness of studying the phenomena using two-fold trigonometric series by normal functions in the rectangular area.

4. Assessing, according to two mutually perpendicular directions, the degree of influence of the plate vibration mode on the fullness of sound energy transmission through a flat barrier.

2. Material and methods

2.1. Sound wave diffraction at cross elastic gyroscope suspension

Supports with elasticity friction are used mainly in systems having limited rotation angles. In practice, such supports do not create a friction torque (as the value of elasticity friction is very low), have low accuracy of fixing the axis direction, but operate satisfactorily under heavy vibration. Depending on a type of elastic element deformation, there are bending supports and torsion supports.

358


A simple ribbon hinge is a plate connecting the fixed element to the moving element. This

hinge is used, for example, as a pendulum suspension. The elastic hinge consists of a lever, two resilient plates and a fixed base. Such a hinge is used for small rotation angles of the moving part (1 ... 2 degrees). The track formed by intersection of extensions of the middle planes

of elastic plates is taken as the rotation centre. Figure 2 shows a cross hinge for two-stage gyroscope suspension 3, which is mounted on

plate 1. Plate 1 is fixed on base 4 with a support consisting of four elastic plates 2, intersecting

at an angle of α = 60º... 90º and attached to base 4 and plate 1. The rotation angle of these hinges may reach 30º.

Fig. 2. A cross elastic hinge for a two-stage gyroscope suspension.

2.2. Cross elastic hinge. Mechanical model of interaction with acoustic radiation

We assume the cross angle 2

radπ

α = and analyse the structure of elastic interaction

of acoustic radiation with a two-stage gyroscope suspension mounted on two cross hinges.

To better understand the nature of this phenomenon, we confine ourselves to consideration of the lowest forms of vibrations only. Moreover, for clarity, it is enough to study the waveform

only in one direction. We suppose that under the influence of an acoustic wave, elastic plates make a bending

movement, taking only the first, lower form. Then, in the normal direction, one will receive

movement 1r and the other −

2r , which are represented as components of

11, zy and

22, zy ,

and enable establishing that the notional pivot axis of the movable part of gyroscope will be

moving along axis Y − ( )21yy + and axis Z − ( )

21zz − (Fig. 3a). If these forms are manifested

in phase at both cross hinges, the angular oscillations occur in respect to the conditional output axis O-O of the device (Fig. 3d). If they are manifested in antiphase, the gyroscope torsional

oscillations occur in respect to Z axis (Fig. 3c). If the first forms of plate flexural vibrations have a form shown in Fig. 3b, the form

of gyroscope movements changes and upon the in-phase movement of the extreme points of O-

O axis, the gyroscope makes the reciprocating movement along Z axis (Fig. 3e), while upon

the antiphase movement the angular oscillations along the output axis occur. Thus, the gyroscope suspension, upon acoustic loading, will produce straight fluctuations

relative to axes, Y, Z and angular oscillations relative to axes X, Z. In this case a two-stage differentiating gyroscope has a bias, whereas a two-stage integrating gyroscope has a systematic drift. Furthermore, the device output signal also shows periodic components.

Leaving aside the issue of passing the acoustic wave through the proper gyroscope, a mechanical model of calculating the interaction of the overpressure wave P10 with the

suspension can be represented in a form of two not interconnected elastic plates affected by a flat monochromatic wave (Fig. 4). Here, 1, 2, 3 are the falling, reflected and transmitted waves

through the first plate, respectively, and 1′, 2′, 3′ − through the second plate.

359


a) b)

c) d)

e)

Fig. 3. A mechanism of elastic interaction of acoustic radiation with the device on an elastic suspension.

A number of issues of the plate dynamics, their physical structure and others under the

influence of acoustic radiation is not completely understood yet. First of all, it refers to consideration of the boundary conditions when studying the plate with finite extent, which leads to an infinite system of equations describing the mechanical model.

Fig. 4. A mechanism of pressure wave passing through an elastic suspension.

A characteristic feature of the geometry of boundary surfaces of elastic bodies is the presence

of angular lines. Based on the formulation of boundary problems in the theory of elasticity in displacements (on the basis of the G. Lame’s vector equation), there are three basic boundary problems, i.e. setting the vector of external forces on the body surface, setting the elastic

360


displacement vector on the body surface, and a mixed problem consisting of the fact that

the forces are set on a part of the boundary surface, and a displacement vector is defined on the rest of the surface.

At present, two approaches have been developed, i.e. the method of homogeneous solutions,

first applied by P. A. Schiff and V. A. Steklov, and the G. Lame’s method of exact solutions. The first became a powerful means of asymptotic analysis of approximate shell theories.

A prerequisite for the revival of the second one was the presence of a coherent theory of infinite systems and the emergence of PCs. Here, it is appropriate to mention the opening of asymptotic expression law by B. M. Koyalovich, which enabled establishing the lack of features in the

expressions for stresses at the corner points and solving the first basic boundary problem. The analysis of flexural vibrations of finite plane bodies, i.e. elastic suspension plates, can also be

carried out using the method described in the works of S. P. Tymoshenko. Its essence is to represent a mechanical disturbance and deflection of the plate as a double row by normal functions in the rectangular region. This method has the simplest mathematical interpretation,

but still enables to investigate the dynamics of finite bodies deep enough. The dynamic

properties of a flat infinite barrier in acoustic field have been studied in [1−7]. Sandwich-type

constructions have been considered in [8−12]. The effect of sound waves on gimbals and other

materials has been discussed in [13−24]. With regard to resonance manifestations in gimbals,

they are usually focused on the impact of pedestal vibration and on the parametric resonance. Such external perturbations as spatial waves has not been studied in terms of manifestations

of gimbals’ local peculiarities. We assume further that the elastic suspension plates have hinge fastenings at the ends, and thus the acoustic radiation energy will be absorbed completely by the oscillating plates, without affecting the adjacent structures.

3. Model of occurrence of plate resonant peculiarities

Transmission of acoustic waves through flat components in a form of infinite plates is

thoroughly described by a simplified mathematical apparatus and significantly reduces analysis effort. This is quite enough for studying certain issues. Study of the dynamics of elastic

interaction between flat barriers and an acoustic wave is limited to such models. However, the approximate simulation modelling process has led to simplifications in which

theoretical and experimental results lead to inconsistent findings. This primarily concerns the

occurrence of local peculiarities. The way out is to maximally approximate simulation models to real designs. In relation to

the studied phenomena, it requires a transition from infinite to finite plates. In this case flexural motion of finite flat bodies is advisable to be studied on the basis

of external impact and plate flexure in a form of trigonometric series in the rectangular area.

Let us consider a bi-dimensional problem. Let us suppose that the plate length is equal to a ,

its width to b , thickness to δ2 and is constant in the cross section. We also assume that the

plate thickness is much less than other dimensions, i.e.: ;2 a<<δ .2 b<<δ

The plate material would be absolutely elastic, homogeneous and isotropic. The length of flexural waves would be more than six times greater than the plate thickness, which would

enable to use the equation of a thin plate. Let us consider an acoustic field to be diffused.

In the light of those simplifications, it can be argued that the lateral sides of area element

with a length of dy and width of dx remain in their motion parallel to xOz and yOz planes

and perpendicular to the median plane (Fig. 5).

361


Fig. 5. A diagram of loading a spatial plate.

Whatever function of coordinates x, y would the plate flexion W be of, it can always be expressed by a two-fold series in the rectangular area in normal functions, i.e.:

b

yn

a

xmWyxW

m n

mn

ππ

sinsin),(1 1

∑∑∞

=

∞

=

= , (1)

where: m = 1, 2, …, n = 1, 2, … are numbers of flexion half-waves along x and y axes,

respectively; ),( yxW is transmission of plate surface with coordinates x, y in the direction of z;

( )tWWmnmn

= (Fig. 6).

It is easy to see that each term of series (1) meets the boundary conditions of:

.0;0;0;0

,0;0;0;0

2

2

0

2

2

0

2

2

0

2

2

0

=∂

∂=

∂

∂==

=∂

∂=

∂

∂==

==

==

==

==

byy

byy

axx

axx

y

W

y

WWW

x

W

x

WWW

(2)

The relations (1) enable to calculate the maximum potential energy M0, which accumulates

in flexural plate deformation. For this purpose, it is sufficient to determine the maximum value of potential energy dM0 of a surface element and then integrate the expression obtained in two

ways:

( ) ( )

( ) ( )( )

( ),

,12

,,2

,,

2

1

2

2

2

2

2

0 0

2

2

22

2

2

0

dxdyyx

yxW

y

yxW

x

yxW

y

yxW

x

yxWDM

b a

∂∂

∂−+

∂

∂

∂

∂+

+

∂

∂+

∂

∂= ∫ ∫

σσ

(3)

where: ( )[ ] 131128

−

−= σδED is cylindrical plate stiffness; E is the modulus of elasticity; σ is

the Poisson’s ratio.

The value of maximum kinetic energy T0 at lateral oscillations of a plate is determined by the formula:

362


( )dxdyyxWT

b a

∫ ∫=

0 0

22

0,

2

1µω , (4)

where: µ is the specific weight; ω is a cyclical frequency.

Fig. 6. Distribution of plate flexures: m, n are numbers of half-waves.

Let us apply the general equation of dynamics to build a differential equation of the plate

in principal coordinates. This gives the following:

112

2

2

2

4

nmmnmnQW

b

n

a

mDW =

++ πµ , (5)

where: ( )1 2 2

2 1 2

2 2 mn

m nD

a bπ µ ω

−

+ =

is a natural oscillation frequency;

11nm

Q is a generalized force.

So, if an incident sound wave P(x, y)would be represented in a form of:

( )b

yn

a

xmPyxP

m n

nm

ππ1

0 0

1 sinsin,11

∑∑∞

=

∞

=

= , (6)

where: 11nm

P is a pressure amplitude of the appropriate form; 1

m , 1n are forms of sound pressure

half-waves occurring both in length and width, then its virtual work will be calculated according

to the formula:

( ) dxdyb

yn

a

xmWtyxPA

b a

mn

ππδδ

1

0 0

1

1sinsin,,∫ ∫= . (7)

Setting for specificity:

( ) ( )[ ]

+−+−=2

cossinexp,,101

πθδθω yxktiPtyxP , (8)

where: P10 is a pressure amplitude; k is a wave number, we obtain:

( )[ ] ( )[

( ) ] ( ) ( )[ ]( ) ( )[ ] ,sincoscosexp

sinexpsincosexp2

cosexp

21

1

221

1

2

21

1

12

1

111011

−−−

−

++−−

−−

+−=

amkbnkSSkbibnS

kaiamSabkiktiPQnm

πθπθθπ

θπθθπ

θδω

(9)

from the expression (7).

When 101<<<m , 10

1<<< n , which corresponds to loading evenly distributed over

the plate area, the formula (9) would be converted to the form:

( ) ( )( )ππ11

1

1110cos1cos1

11

nmnmabPQnm

−−=

−

. (10)

363


The generalized force Q will be zero for even values m1 and n1, i.e.:

011

=nm

Q . (11)

And vice versa, for odd values:

( ) 12

11104

11

−

= πnmabPQnm

. (12)

By calculating the maximum work A0 of an incident sound pressure wave, according to the

formula:

( ) ( )dxdyyxWyxPA

b a

,,

0 0

0 ∫ ∫= , (13)

let us establish the law of plate flexural vibrations on the basis of extreme properties of its

bending:

( ) 0000=+−

∂

∂AMT

Wmn

. (14)

If consideration of energy dissipation due to the internal friction is required, it would be

enough to consider the work of these forces in the expression (14), i.e.:

( ) 00000=−+−

∂

∂RAMT

Wmn

, (15)

where:

( ) ∑∑∫ ∫∞

=

∞

=

==

1 1

22

0 0

2

0

8

1,

2 m n

mn

b a

WabdxdyyxWR ωµηχ

, (16)

2

mnηµωχ = is an internal friction coefficient; η is a coefficient of losses.

Let us suppose that mm =1

, nn =1

.

These conditions imply the coincidence of a number of acoustic radiation half-waves and

plate vibration generated in two directions: along axis x ( mm =1

) and along axis y ( nn =1

).

Substituting the relation (1), (8) in the expressions (3), (4) and (13), we obtain the following:

( )yxWb

n

a

mBabM

m n

mn,

8

1

1 1

2

2

2

2

2

4

0 ∑∑∞

=

∞

=

+= π ,

( )yxWabTm n

mn,

8

1

1 1

22

0 ∑∑∞

=

∞

=

= ωµ , (17)

( )yxWPabAm n

mnmn,

4

1

1 1

0 ∑∑∞

=

∞

=

= .

On the basis of the extrenality condition (15), the expressions (17) give an opportunity to find out the value of bend for each pair of indices m and n:

( )( )22

,

ωωµ −

=

mn

mn

mn

PyxW , (18)

where mnω is a natural frequency calculated from the above formula.

It is clear that under the occurrence of mnωω = , the plate flexure constantly grows and it

becomes acoustically transparent.

Substituting the value of generalized force mn

Q (19) in the differential equation of motion

(5), the law of plate flexural vibrations can be established on the mnform at the continuous action of sound radiation in a time interval [0, t]. It contains its natural and forced vibrations, i.e.:

364


( ) ( )

( )[ ] ( )

( ) ( )[ ] ( )

( )( ) ( )[ ]( ) ( )[ ] .sincos

cosexpsinexp

2sincosexp

sin,,

12

1221222

12

21

1

2

1

1

10

0

11

11

−

−−

−−−

−−

++−×

×+−−×

×

++−−+=

=−= ∫

amkbnk

abmnSSkbibnSkaiamS

ttgabktiP

dtttQtyxW

mn

t

mnmnmnmn

πθπθωωµ

πθπθπ

ϕπ

θθδω

ωµω

(19)

Finally, considering the relation (19) we obtain:

( ) ( )

( ) ( )( ) ( )[ ]( ) ( )[ ]

( )[ ] ( )

( ) ( )[ ] ( )

,sinsin

cosexpsinexp

2sincosexp

sincos

sinsin,,,,

12

21

1

2

1

1

1 1

12

1221222

10

1 1

b

yn

a

xm

abmnSSkbibnSkaiamS

ttgabkti

amkbnktP

b

yn

a

xmtyxWtyxW

m n

mn

m n

mn

ππ

πθπθπ

ϕπ

θθδω

πθπθωωµρ

ππ

×

×+−−×

×

++−−+×

×++−=

==

−−−

∞

=

∞

=

−

−−

∞

=

∞

=

∑∑

∑∑

(20)

from the expression (1),where: ( ) ( ) ( )[ ]21

212

sinsincoscos tttttmnmnmn

ωωωωωωρ−

−+−= ;

( ) ( )( ) 11coscossinsin

−−

−−= ttttttgmnmnmn

ωωωωωωϕ .

The same is for the case of acoustic loading uniformly distributed over the plate area. For this purpose, it is enough to substitute the relations (12) in (5). We obtain:

( ) ( ) ( )tmngPtyxWmnmnmn

ωωπµ cos116,,1

22

10−=

−

. (21)

Now the pattern of plate flexural motion can be established:

( ) ( ) ( ) ( )b

yn

a

xmtmngPtyxW

mn

m n

mn

ππωωµπ sinsincos116,,

1 1

12

12

10−= ∑∑

∞

=

∞

=

−−

, (22)

where m and n are odd numbers. For a finite plate, the flexural motion can be represented as the superposition of forced

vibrations of an infinite plate and natural vibrations that occur in the plate given its size. If a plate impedance on the mn form is:

( ) ( )[ ]214

1

3

1sin

mnmnmnmncciVPZ ωωθµω −−−

−== , (23)

then it becomes clear that − even fulfilling the wave coincidence condition θ1

3sin

−

= cc , but

if there is no equality of frequencies ωmn of finite plate natural vibrations and frequencies ω

of infinite plate forced vibrations − the flexures would have a fixed value. The plate would be

acoustically transparent, i.e. the equality 0=mn

Z would occur only if both conditions are

fulfilled:

.

,sin1

3

mn

cc

ωω

θ

=

=−

(24)

365


4. Discussion of results of plate flexures by vibration forms

Let us perform a numerical analysis of lower vibration forms, having assumed the following

parameters for the sake of clarity: 32 2 10 ,mδ

−

= ⋅ 0,3,σ = 2710 .E Nm

−

= ,4rad

πθ = 1

100 ,sω−

=

0,1 ,а m= 0,2 .b m= The quantitative analysis shows that the maximum deflection of an elastic

suspension plate is observed at the first (lowest) waveform, that is when 1

1,k

m m= = 1

1.k

n n= =

Higher waveforms have a more complex structure of the bending motion. For example, upon

1 11 , 2,

k km m n n= = = = each of the plates has, unlike the first form, two local extrema

of opposite polarity, while upon 1 1

1 , 3k k

m m n n= = = = they have three extrema. The higher

the form number, the more complex the bending movement of the suspension plates. Obviously,

the number of extrema is determined by the product .

k km n⋅

The analysis shows that upon an odd n, the bend magnitude is much larger in absolute terms than upon an even n. Thus, these forms will contribute to a more intense sonic energy pumping. The numerical values of maximum plate flexures for the first five forms of vibration are shown

in Table 1. The values of natural frequencies mnω of vibration

k km n − forms are shown in

Table 2. Here, P10 is a normalizing factor.

The numerical analysis proves that the maximum plate flexures are on the first − the lowest

− form, i.e. when 1

1;m m= =1

1.n n= =

Thus, the most favourable for the device is a combination of 1 waveforms of one plate with even waveforms of the other one, i.e. 2, 4, 6, etc. (Fig. 7a). In this case, as can be seen, the

movement of the device output axis in the direction of Y axis is only due to fluctuations of the

first plate 1r , and there is no movement towards Z axis. If there is a combination of the first

waveform of one plate and odd forms (1, 3, 5, 7, etc.) of the other, there is the most complex

motion of the suspension axis, both in the direction of Y axis and in the direction of Z axis (Fig. 7b). There is both translational and angular acoustic suspension vibration.

a) b)

Fig. 7. The effect of a plate waveform on the movement of the device output axis.

Table 1. The maximum plate flexures.

m = m1 n = n1 Wmax/P10, m

1 1 15

1 2 12*10−4

1 3 4,8

1 4 5,9*10−4

1 5 2,9

2 2 11,8*10−4

3 3 4,8

4 4 5,6*10−4

5 5 2,9

366


Table 2. The values of natural plate frequencies.

m = m1 n = n1 mnω , s-1 m = m1 n = n1

mnω , s-1

1

1 0,376

4

1 4,888

2 0,602 2 5,114

3 0,978 3 5,490

4 1,504 4 6,016

5 2,181 5 6,693

2

1 1,278

5

1 7,595

2 1,504 2 7,821

3 1,880 3 8,197

4 2,406 4 8,723

5 3,083 5 9,340

3

1 2, 782

2 3,008

3 3,384

4 3,910

5 4,587

Thus, the elastic interaction of a gyroscope suspension with acoustic radiation perturbs the device motion and, consequently, leads to the emergence of measurement errors. The most

dangerous are odd vibration forms, which transmit maximum sound energy

5. Conclusions

The research show that, regarding the operating conditions, the base element of gimbals and

its components goes into the category of impedance structures interacting elastically with penetrating acoustic radiation. Therefore, the on-board equipment needs to be placed in acoustic comfort.

Methods for solving this task depend on what is more important - high positioning accuracy or weight of the missile/aircraft.

Finally, special attention should be paid to the risk of resonance phenomena, in particular the spatial-frequency resonance. Ways to solve this problem have not yet been sufficiently

developed, because of the spatial nature of N-wave and penetrating radiation, unlike force and kinematic impacts penetrating into devices only through supports.

Acknowledgements

The Industrial Research Institute for Automation and Measurements is kindly acknowledged for covering the costs of publishing of the paper.

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Dec. 12, 2016; accepted on Jan. 30, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0032.



IMPEDANCE SENSORS MADE IN PCB AND LTCC TECHNOLOGIES

FOR MONITORING GROWTH AND DEGRADATION OF PSEUDOMONAL

BIOFILM

Konrad Chabowski1), Adam F. Junka2), Tomasz Piasecki1), Damian Nowak1),

Karol Nitsch1), Danuta Smutnicka2), Marzenna Bartoszewicz2), Magdalena Moczała1),

Patrycja Szymczyk3)

1) Wrocław University of Science and Technology, Faculty of Microsystem Electronics and Photonics, Z. Janiszewskiego 11/17, 50-372 Wrocław, Poland ( [email protected], +48 71 320 3223, [email protected], [email protected], [email protected], [email protected]) 2) Medical University of Wrocław, Department of Pharmaceutical Microbiology and Parasitology, Borowska 211a, 50-556 Wrocław, Poland ([email protected], [email protected], [email protected]) 3) Wrocław University of Science and Technology Centre for Advanced Manufacturing Technologies, I. Łukasiewicza 5, 50-371 Wrocław, Poland ([email protected])

Abstract

The suitability of low-cost impedance sensors for microbiological purposes and biofilm growth monitoring was

evaluated. The sensors with interdigitated electrodes were fabricated in PCB and LTCC technologies.

The electrodes were golden (LTCC) or gold-plated (PCB) to provide surface stability. The sensors were used for

monitoring growth and degradation of the reference ATCC 15442 Pseudomonas aeruginosa strain biofilm in in-

vitro setting. During the experiment, the impedance spectra of the sensors were measured and analysed using

electrical equivalent circuit (EEC) modelling. Additionally, the process of adhesion and growth of bacteria on a

sensor’s surface was assessed by means of the optical and SEM microscopy. EEC and SEM microscopic analysis

revealed that the gold layer on copper electrodes was not tight, making the PCB sensors susceptible to corrosion

while the LTCC sensors had good surface stability. It turned out that the LTCC sensors are suitable for monitoring

pseudomonal biofilm and the PCB sensors are good detectors of ongoing stages of biofilm formation.

Keywords: Pseudomonas aeruginosa, biofilm, interdigitated sensor, impedance spectroscopy.


1. Introduction

The vast majority of microorganisms exist as attached and organized communities referred to as biofilms [1]. These communities are predominantly embedded within various extracellular polymeric substances (sugars, proteins, DNA) also known as a “biofilm matrix” [2]. The matrix

serves microorganisms as a shelter and a shield protecting them from not only drugs and other xenobiotics but also from activity of the immune system. The biofilms are able to form on

virtually every type of surface, including tissues and abiotic biomaterials used for medical purposes [3]. It is estimated that biofilms are responsible for up to 80% of nosocomial infections [4]. Therefore, there is an urgent need of developing new tools for rapid detection of “medical

biofilm” enabling to apply suitable eradication procedures. The tools designed for rapid detection of biofilms may be helpful in virtually all flow systems

endangered by the development of microbes. Among the examples of such systems in nosocomial settings are indwelling catheters, nutrition accesses or hospital water distribution pipes [5]. The usage of impedance sensors providing possibilities of non-invasive, label-free

and real-time measurements is promising in the above mentioned clinical situations. Using the sensors combined with the impedance spectroscopy method for detecting attachment

K. Chabowski, A. F. Junka, et al.: IMPEDANCE SENSORS MADE IN PCB AND LTCC TECHNOLOGIES …

of microbial cells and biofilm formation has been already reported by other authors who tested

the impedance potential using such nosocomial strains as Escherichia coli [6−9],

Staphylococcus aureus [7, 10, 11], Staphylococcus epidermis [11, 12], Pseudomonas aerugino-

sa [5, 13−15], Bacillus subtilis [13] and Salmonella typhimurium [9, 16]. The impedance micro-sensors with interdigitated electrodes were used for this purpose by

some researchers [9, 11, 12, 17] because of their advantages: a small size enabling to perform small-scale experiments using very small samples, fast establishment of a steady-state signal,

a low ohmic drop of potential, an increased signal-to-noise ratio and − last but not least − higher

sensitivity comparing with conventional-size macro-electrodes. Typical sensors with interdigitated electrodes designed for microbiological sensing are

usually fabricated using the lithography technique on silicon and glass substrates [18]. The main

disadvantages are their high cost and complicated process of manufacturing. The sensors made in the printed circuit board (PCB) technology may be a promising

alternative as they are cost-effective and relatively easy to manufacture [19]. The PCB sensors were already employed in microbiological, oncologic or immunologic applications, namely for:

bacteriuria screening [7], analysis of colorectal carcinoma cells [20] and Interleukin-12 detection [19, 21]. The sensors made in low temperature co-fired ceramics (LTCC) could be also a constructive option. LTCC devices were reported to be used in microbiological

applications, i.e. monitoring cell cultures [22], monitoring water solutions [23], monitoring glucose concentration [24], an electronic tongue [25] and cortisol detection [26]. However, the

mentioned devices used mostly voltamperometric measurement systems, avoiding the impedance spectroscopy.

In the impedance spectroscopy the electrical equivalent circuit modelling is a method

of analysing impedance spectra [27]. It consists in the numerical fitting of the electrical equivalent circuit (EEC) impedance to the measured impedance spectrum. As specific

components of the EEC are correlated with various conduction and polarisation processes, such an approach enables to identify and separate them. This method is not widely used in analysis of the impedimetric sensors’ responses in microbiological applications despite of the fact that

it may provide detailed information about the measured object [14, 17, 28, 29]. The aim of this work was to combine advantages of the interdigitated electrodes with the

cost-effective PCB technology and the more accurate LTCC technology, and to determine whether such sensors may be used for detection of the P. aeruginosa biofilm presence and for monitoring particular stages of this structure formation. The presented research is related to the

authors’ previous work [17], in which impedance micro-sensors on glass substrates were used.

2. Materials and methods

2.1. Preparation of impedance sensors

The layout of impedance sensor interdigitated electrodes was designed using CadSoft Eagle

software. Each electrode consisted of five digits with 1.9 mm length and 0.25 mm width. The distance between electrodes was 0.25 mm. Sensors in the PCB technology were fabricated in

Satland Prototype (Gdańsk, Poland) on a glass-reinforced epoxy laminate (FR4 type) commonly used for electronics purposes. The copper layer on the laminate was 35 μm thick. The electrodes were electroplated with gold to improve surface stability (Fig. 1a). Sensors in

the LTCC technology were formed using 4 layers of green tape (DP 951, DuPont). To obtain an appropriate shape of each layer, the laser beam cutting (LPKF Protolaser U cutting system) was

performed. The metallic electrodes and their conductive paths together with contacts were screen-printed (Au conductive paste ESL 8880-H, Electroscience Laboratories) on the last ceramic layer. Additional ceramic layers were then applied to insulate electrode leads (Fig. 1b).

370


Fig. 1. An impedance sensor fabricated in: the PCB technology (a); the LTCC technology (b);

a close-up view of sensing area dimensions (c); sensors inserted in sockets (d).

Due to a low cost of production all sensors were disposable. The dimensions and thickness

of PCB and the distance between contacts enabled to mount a sensor directly in a micro-USB connector (Fig. 1d).

2.2. Impedance spectroscopy measurement setup

The impedance spectra were measured in a frequency range from 0.1 Hz to 100 kHz with 25 mVrms excitation signal using an IMP-STM32 [30] impedance analyser and applying an

accelerated method for low frequency impedance evaluation [31]. The impedance analyser was linked with a 24-channel multiplexer designed to accommodate a 24-well titrate plate and

enabling sequential switching between up to 24 impedance sensors placed vertically in the titrate plate wells (Fig. 2a).

Prior to any experiments the sensors were cleaned using distilled water and acetone to

remove any residue and sterilized with isopropyl alcohol. Then, they were aseptically placed into sockets of the multiplexer and irradiated with UVC light for 20 minutes.

All devices were controlled by a home-built software ImpeDancer. A measurement setup and an incubator in which the experiment was performed are presented in Fig. 2b.

2.3. Pseudomonal strain preparation

A reference P. aeruginosa ATCC14454 strain was used for experimental purposes. The ability of the aforementioned strain to form a biofilm on abiotic surfaces has been already recognized in the authors’ previous work [17]. An overnight culture of the examined strain was

diluted to 1 McFarland using a densitometer (Biomerieux, Poland) and subsequently diluted to 106, 104, 102 colony forming units per millilitre (cfu/ml) in the Tryptic Soy Broth (TSB, Becton

Dickinson) medium.

a) b)

Fig. 2. A measurement setup: components of the measurement setup: a personal computer,

an impedance analyser (left) and a 24-channel multiplexer with a titrate plate (right) (a);

the 24-channel multiplexer placed inside an incubating chamber (b).

371


2.4. Impedance measurements

The measurements of impedance spectra were carried out using P. aeruginosa –

contaminated TSB (106, 104 and 102 cfu/ml) and pure TSB as a reference. 4 rows of the titrate

plate consisting of 6 wells each were filled with 2 ml of the medium each and placed in the multiplexer. This setup was incubated for 168 hours at 37ºC, 95% RH. A single impedance

spectrum measurement took 60 s which made the measurement repetition time of appro-ximately 24 minutes for each specific impedance sensor.

The experiment was performed separately for PCB and LTCC sensors.

2.5. Crystal violet colouring

The goal of the crystal violet colouring experiment was to visually assess the attachment

of P. aeruginosa biofilm to the surface of PCB sensor. It was prepared in a similar way to the

impedance measurements but only the 106 cfu/ml P. aeruginosa suspension was used. The sensors were incubated for 1, 4, 16 and 24 h at 37ºC. After these times of incubation the sensors

were aseptically removed from the multiplexer, rinsed with distilled water and left to dry in room temperature. Next, the sensors were immersed in 1 ml of a 0.1% solution of crystal violet in water (ProLab Diagnostics) for 5 minutes, rinsed thoroughly with distilled water to

remove excess stain and left in room temperature to dry.

2.6. SEM and EDS

The morphology studies were performed with a field emission gun scanning electron

microscope (SEM) with a germanium ion source (Dual Beam, Helios NanoLab™600i, FEI). The composition of individual layers of the gold-plated copper electrode was determined using

the Energy-dispersive X-ray spectroscopy (EDS, EDAX detector) on a sample that was previously milled at an angle using the focused ion beam (FIB).


3.1. Crystal violet colouring and optical microscopy

The results of crystal violet colouring are shown in Fig. 3. The bacteria attachment and the start of biofilm formation on the surface was visible after 4 hours of incubation. After 16 hours about a quarter of the surface was covered with a biofilm, while after one day of incubation the

whole surface was covered by a mature, three-dimensional thin pseudomonal biofilm structure (Fig. 3d).

a) b) c) d)

Fig. 3. Optical microscopy images (magnitude 40 x) of P. aeruginosa biofilm stained with a crystal violet on the surfaces of PCB sensors after: 1 hour (a); 4 hours (b); 16 hours (c) and 24 hours of incubation (d).

372


3.2. SEM imaging

The results of SEM imaging of LTCC sensor are shown in Fig. 4. Similarly to the PCB sensor

after 16 hours of incubation the sensor’s surface was partly covered with a three-dimensional

biofilm structure, however the presence of a bacterial monolayer cannot be proven. a) b) c)

Fig. 4. SEM images of P. aeruginosa biofilm on the surfaces of LTCC sensors: a clean reference (a);

after 16 h of incubation (b) and focused on a biofilm structure (d).

3.3. Impedance spectra

Examples of impedance spectra obtained during the experiment with P. aeruginosa strain with 102 cfu/ml initial concentration for both sensor types as well as the reference (pure TSB) during first 36 hours of incubation (biofilm formation) and last 132 hours (biofilm degradation)

are shown in Table 1. Significant changes in the electric properties of sensors in both the bacterial culture and the reference were observed.

3.4. Electrical equivalent circuits

Basing on the literature [9, 14, 28, 29, 32], the measured impedance spectra and knowledge about the physiochemical properties of biofilm [5, 6, 8, 16], the electrical equivalent circuits

(EEC) were obtained and are shown in Fig. 5. The sensors made in PCB and LTCC technologies differed in the electrode materials and

morphology which caused also differences in analysis of the impedance spectra. For the LTCC sensors it was impossible to distinguish the interfacial from biofilm capacitance, therefore a simplified EEC was used (Fig 5b).

Each component of the model represents a different phenomenon of current conduction or Polarization, i.e. RS – a liquid medium resistance, CPEB – a constant phase element which

models the surface of non-uniform electrodes and their coverage by the biofilm, RB −

a resistance of the surface of electrodes and the biofilm pores, CI – an electrical double layer interfacial capacitance, RCT – a charge transfer resistance. The model contains a constant phase

element (CPE) which is widely used in the equivalent circuit modelling of impedance spectra

[27]. Its admittance YCPE depends on a radial frequency ω and two parameters − Q and n:

n

CPEjQY )( ω∗= . (1)

If the parameter n goes to 1 the admittance of CPE becomes similar to the admittance

of capacitor.

373


Table 1. Typical impedance spectra of sensors placed in a medium with P. aeruginosa strain (102 cfu/ml initial concentration). Black arrows point to changes of impedance spectra in time.

Stage\Sensor PCB LTCC

Biofilm formation

Biofilm

degradation

Reference

a) b)

Fig. 5. Electrical equivalent circuits of PCB (a) and LTCC (b) sensors placed in a medium with bacteria.

374


3.5. Electrical equivalent circuit analysis of PCB sensors The impedance spectra obtained in the experiment were analysed using ZView software

(Scribner) and EEC modelling using the EEC shown in Fig. 5a. Each experiment was repeated 6 times. Changes of the calculated mean values and standard deviations of EEC parameters

during 168 hours of incubation are shown in Fig. 6a-6f while a result of the impedance spectra fitting is shown in Fig 6g.

The most eye-catching EEC parameter is RCT. For the PCB sensors in P.aeruginosa-

containing wells a rapid rise of RCT can be observed in the third, fifth and seventh hour of measurement for 106, 104 and 102 cfu/ml initial concentrations, respectively. The RCT value

for sensors in P.aeruginosa with lower initial concentrations achieves a quasi-plateau state while for the reference it slowly decreases. This parameter is a sensitive indicator of the moment, when the area of sensor’s electrodes is fully covered by the biofilm because the biofilm

can be regarded as an electrical insulator [29].

a) b) c)

d) e) f)

g)

Fig. 6. Changes of mean value (points) and standard deviation (error bars) of EEC parameters in time during

incubation: RCT (a); RS (b); CPEB-Q (c); CPEB-n (d); CI (e); RB (f); and examples of measured (dots)

and fitted (lines) impedance spectra for 102 cfu/ml at 36th hour (g).

The value of liquid resistance RS almost continuously decreases in samples with

P.aeruginosa while for the reference it achieves a plateau state between the fourth and sixteenth

hours – then it decreases too − probably because of the increased ionic concentration caused

375


by corrosion of electrodes. Additionally, the behaviour of CPEB is very interesting. The values

of Q and n parameters of CPEB in the first stage of measurement fluctuate for each data series. The situation becomes stable in the eighth hour of measurement when CPEB-Q slowly decreases for sensors in P.aeruginosa solution and after the thirty-second hour it increases again, while

for the reference it grows continuously. The same situation − inversely − occurs for the CPEB-

n parameter values. The CI and RB seem to not carry any useful information as changes of their values were observed also in the reference and values of their standard deviations are quite

high.

3.6. Electrical equivalent circuit analysis of LTCC sensors

As previously, the impedance spectra obtained in the experiments repeated 6 times were

analysed using ZView software (Scribner) and EEC modelling using the EEC simpler than that in the case of PCB sensors, shown in Fig. 5b. Changes of the calculated values of EEC

parameters during 168 hours of incubation are shown in Fig. 7a − 7d while a result of the impedance spectra fitting is shown in Fig. 7e.

In this case the most important EEC component is CPEB, which clearly reflects a current

state of pseudomonal biofilm. The adhesion stage is finished during first hours of the

experiment and − depending on the initial cell concentration − goes to the growth phase which is represented by a constant growth of CPEB-Q value and a corresponding decrease of CPEB-n

value. About the 36th hour (depending on the initial concentration) the biofilm enters the degradation phase resulting in a smooth decrease of CPEB-Q value and a slow growth of CPEB-n value. There should be noted that the CPEB reference value is quasi-constant during the whole

experiment.

a) b) c)

e) f)

Fig. 7. Changes of mean value (points) and standard deviation (error bars) of EEC parameters in time during

incubation: CPEB-Q (a); CPEB-n (b); RS (c); RB (d); and examples of measured (dots) and fitted (lines)

impedance spectra for 102 cfu/ml at 36th hour (e).

376


A plot of RS values does not show any significant difference between the biofilm and

reference. Similarly, RB with one additional phenomenon – in the first 30 hours of experiment

the RB reference value exceeds 10 MΩ, then decreases and − after about 80 hours − achieves the same level as the rest. It is caused by the lack of bacterial biofilm in the reference and probably slow adhesion of TSB nutrients to the sensor surface which creates some kind of a

conductive layer between electrodes.

3.7. SEM and EDS examination of PCB electrodes

As shown in Sections 3.3 and 3.5 the impedance spectra of reference sensors and their EEC

parameters varied in time. It may suggest that − despite the absence of bacteria − the sensor’s surface degrades in a corrosive environment. To examine that possibility a single sensor

prepared as in Section 2.2 was incubated in 0.9% NaCl aqueous solution for 48 hours. This solution in respect of a corrosive factor is very similar to TSB but does not leave any residue on the sensor.

Fig. 8. A SEM image of a sensor’s gold-plated electrode after incubation in 0.9% NaCl aqueous solution

for 48 hours. Corrosion of metal layers under gold plates can be seen.

Fig. 9. A SEM image of a sensor’s electrode etched by FIB and EDS place marked red (left).

The elemental results of EDS analysis (right).

The sensor surface after incubation was assessed using SEM (Fig. 8). In several points the pitting corrosion of the electrodes can be seen. It means that the gold layer was not tight and in

a pure corrosive environment corrosion of the electrodes can occur, influencing the EEC parameters.

A typical gold-electroplated metallic layer of PCB consists of three layers in a sandwich

structure: copper, nickel-phosphorus alloy and − finally − gold [32]. The percentage of each mentioned element in the sensor’s electrode was checked using the EDS analysis. Firstly, the sensor was prepared as described in Section 2.2 and then milled using the focused ion beam

(FIB), as shown in Fig. 9. Then, the EDS analysis was performed. The obtained results confirmed a sandwich structure of metal layers – copper is the bottom one, covered by nickel-

phosphorus and gold. As can be seen in Fig. 8. and in Table 2, the percentage of gold layer is very low. In effect the gold layer is not tight and the metallic layers under it are not protected

from corrosion.

377


Table 2. The chemical composition of PCB sensor’s electrodes.

Element Orbital Weight [%] Atomic [%] Error [%]

carbon K 2.66 11.91 9.56

phosphorus K 5.54 9.61 7.43

nickel K 36.27 33.17 0.96

cuprum K 52.70 44.54 1.02

gold L 2.82 0.77 3.17

4. Conclusions

The research presented in this study concerned the application of impedance sensors fabricated using the PCB and LTCC technologies in detection and monitoring of pseudomonal

biofilm development and degradation. During the experiments the impedance spectra (0.1 Hz – 100 kHz) of the sensors placed in a TSB medium with and without P. aeruginosa bacteria

were measured in approximately half-hour intervals. The obtained data were analysed and the EEC was built (Fig. 5). It enabled to identify various processes of conduction and polarization.

For biofilm monitoring using PCB sensors the most notable element of EEC was RCT which

represented the charge transfer resistance. As can be seen in Fig. 6a, its value grew rapidly after a few hours of incubation of the sensor in the medium with bacteria while RCT of the reference

(pure medium) was slowly decreasing. This moment was strictly connected with the complete biofilm coverage of the electrodes which caused a decrease of the charge transfer. These results were coherent with the images of crystal violet stained biofilm obtained using the optical

microscopy (Fig. 3). Due to limitations of the traditional PCB technology the rest of EEC parameters were highly influenced by additional phenomena occurring during the experiment.

The most notable side-effect was corrosion of Ni and Cu layers placed under a non-tight gold electroplating of the electrodes. Evidently, the quality of the gold layer on the PCB was worse than it can be achieved e.g. by sputtering [33]. The effects of corrosion were assessed using

SEM (Fig. 8). Despite that, the research results presented in this report show that the impedance sensors fabricated using the cheaper and simpler PCB technology are still very useful for

marker-less in-situ detection of the biofilm formation. There were interesting the capacitive parameters of EEC components for PCB sensors: the

Q and n parameters of CPEB and CI capacitance (Fig. 6c, 6d and 6e). These values became

quasi-stabilised after approximately eight hours for sensors in the bacterial medium, whereas for the reference they are changing all the time. CPEB and CI depended mostly not on the

bacterial biofilm state but on corrosion of the electrodes − in this case the bacterial biofilm

serves as an corrosion inhibiting layer. For biofilm monitoring using LTCC sensors the most notable element of EEC was CPEB

which clearly reflects a current state of pseudomonal biofilm – the adhesion, growth and degradation stages (Fig. 7a and 7b). Thanks to the lack of corrosion effect this kind of sensor can be successfully applied to such purposes.

The obtained results were coherent with the authors’ previous work [17], where micro-sensors fabricated using the thin film technology with pure gold interdigitated electrodes on

a glass substrate were employed. The common features were a characteristic step-growth of the

value of parallel resistance EEC element − like in analysis of PCB sensors, and a change of CPE

element modelling electrodes’ surfaces when the biofilm entered the growth phase − like in analysis of LTCC sensors.

378


Acknowledgements

This work was supported by Wrocław University of Technology statutory grant.

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Aug. 03, 2016; accepted on Dec. 16, 2016; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0028.



MEASUREMENT OF SURFACE PROFILE AND SURFACE ROUGHNESS

OF FIBRE-OPTIC INTERCONNECT BY FAST FOURIER TRANSFORM

Chern S. Lin1), Shih W. Yang2), Hung L. Lin1), Jhih W. Li1)

1) Feng Chia University, Department of Automatic Control Engineering, 100 Wenhwa Road, Seatwen, Taichung, Taiwan ( [email protected], +886 4 2451 7250 3900, [email protected], [email protected]) 2) National Chiao Tung University, College of Electrical and Computer Engineering, 1001 University Road, Hsinchu, Taiwan ([email protected])

Abstract

This study proposes a surface profile and roughness measurement system for a fibre-optic interconnect based

on optical interferometry. On the principle of Fizeau interferometer, an interference fringe is formed on the fibre

end-face of the fibre-optic interconnect, and the fringe pattern is analysed using the Fast Fourier transform method to reconstruct the surface profile. However, as the obtained surface profile contains some amount of tilt, a rule for

estimating this tilt value is developed in this paper. The actual fibre end-face surface profile is obtained by

subtracting the estimated tilt amount from the surface profile, as calculated by the Fast Fourier transform method,

and the corresponding surface roughness can be determined. The proposed system is characterized by non-contact

measurement, and the sample is not coated with a reflector during measurement. According to the experimental

results, the difference between the roughness measurement result of an Atomic Force Microscope (AFM) and the

measurement result of this system is less than 3 nm.

Keywords: surface profile, surface roughness, fibre end-face, Fast Fourier transform.


1. Introduction

Fibre-optic communication has become the main media of the present communication transmission. For example, the fibre-optic interconnect technology “Thunderbolt” released by

Intel transmits data as light signals via optical fibre instead of copper wire [1−2], so the optical

fibre and traditional USB joint are interconnected to increase the transmission rate. The Thunderbolt technology has a key fibre-optic interconnect. The entire fibre module comprises

three connectors: an optical/electric conversion part (O/E part), a receptacle lens (Re-Lens), and a plug lens. The O/E Part is a connector for the O/E module and optical fibre, laser cut optical fibres are directly inserted in four holes in the front end of the O/E Part, and the end faces

of these fibres and the holes are aligned with a co-plane (fibre tips were not polished), as shown in Fig. 1.

Fig. 1. The O/E Part and a fibre end-face measured in this study.

C. S. Lin, S. W. Yang, et al.: MEASUREMENT OF SURFACE PROFILE AND SURFACE …

The fibre end-face roughness after laser cutting has a significant influence on the

transmission quality of light signals [3−4]. If the fibre end-face roughness is small, the

efficiency of fibre optic coupling is higher. Therefore, developing an efficient system for measuring a surface profile and surface roughness of a fibre end-face is an important issue. Using a contact measurement equipment to check the roughness of fibre end-face is a high-

precision scheme [5−6], and as the determinant scan requires a long processing time, the contact probe may scratch the fibre end-face.

The non-contact measurement is another feasible method. In measurement of an insertion loss the laser light shoots into the photovoltaic component joint [7], and the loss value of optical power is indirectly measured to evaluate the quality of fibre end-face. However, to further

understand the surface profile and roughness of the optical fibre cutting end-face, combining

the machine vision technology with optical interferometry is another appropriate option [8−12]. The phase shifting interferometry shall capture and analyse multiple fringe patterns in order to

reconstruct a three-dimensional surface profile of the sample [13−15], where the number of computations is large, but the measurement accuracy is quite high. The Fourier Transform method can reconstruct the surface profile of sample by using only one fringe pattern. Tien et

al. [16−17]. used a Fizeau interferometer and a Twyman-Green interferometer to obtain

interference fringes of thin film, and applied the Fourier Transform method to measure the surface profile and residual stress of thin film [15, 17]. This type of measurement algorithm

based on analysing one fringe pattern is faster. To sum up, this study uses the optical interferometry and a novel imaging system to measure

the surface profile and surface roughness of a fibre end-face on an O/E Part [18−19]. The camera captures a fringe pattern of the fibre end-face, and the fringe pattern is analysed using the Fourier transform method to reconstruct the surface profile [19]. However, the obtained

surface profile has an additional tilt information, therefore this study proposes a method to eliminate the tilt. Finally, the tilt value is subtracted from the surface profile obtained by the Fourier Transform method, to obtain the actual fibre end-face profile, and the corresponding

surface roughness is determined. The difference of RMSs between the roughness measurement results of the proposed method and those obtained by an Atomic Force Microscope (AFM)

is less than 3 nm.

2. Optical interferometry and novel imaging system

Based on the principle of Fizeau interferometer, the interference fringes of a local fibre end-

face on an O/E Part can be observed and recorded by a CCD camera. The proposed image

processing algorithm for measuring the surface profile and surface roughness of a fibre end-face is described in the following sections.

2.1. Fringe contrast enhancement

Enhancing the contrast of an interference fringe contributes to the accuracy of the obtained phase distribution. The vertical direction of the surface is detected. A hundred images are collected with an adjustable holder used in image acquisition. Therefore, the contrast of the

fibre end-face fringe (Fig. 2a) is enhanced according to the concept of Gamma Correction [20]. A relationship between the fringe grey levels before and after the contrast enhancement is:

( 1)

( , )( , ) ( ) ,

255

oI x y

I x yγ

γα β

−

= + (1)

382


where: ( , )oI x y is an original fringe grey level; ( , )I x y is a fringe grey level after the contrast

enhancement; γ is a correction factor and 0γ > ; α and β are user-defined scale parameters.

When 1γ > , a bright fringe in Fig. 2a becomes dark; when <1,γ a dark fringe in Fig. 2a

becomes bright. After testing, in this study a correction factor γ equal to 0.7 was chosen

in order to obtain an appropriate contrast in the darker part. The corresponding results are shown

in Fig. 2b. In the darker part the contrast of images (b) is better than images (a). a) b)

Fig. 2. An original fringe pattern of a local fibre end-face (a);

the contrast enhancement result of γ equal to 0.7 (b).

2.2. Phase extraction using Fast Fourier Transform

According to the Fourier Transform method, as proposed by Takeda et al. [19], the intensity distribution of a parallel fringe obtained by introducing a spatial carrier can be expressed as:

, ,

( , ) ( , ) ( , ) cos[2 2 ( , )],c x c y

I x y a x y b x y f x f y x yπ π φ= + + + (2)

where ( , )a x y is a background signal of the fringe pattern; ( , )b x y is an amplitude of the

interference fringe; 0,xf and

0, yf are spatial frequencies in x and y directions, respectively and

( , )x yφ is a required phase distribution.

According to the Euler’s formula, (2) can be expressed as:

*

, , , ,( , ) ( , ) ( , ) exp( 2 2 ) ( , ) exp( 2 2 ),

c x c y c x c yI x y a x y c x y j f x j f y c x y j f x j f yπ π π π= + + + − − (3)

where: 1

( , ) ( , ) exp[ ( , )];2

c x y b x y j x yφ= * 1( , ) ( , ) exp[ ( , )];

2c x y b x y j x yφ= − and * represents

a conjugate complex number.

In order to extract the phase distribution, (3) is processed by Fast Fourier Transform to obtain:

*

, , , ,( , ) ( , ) ( , ) ( , ),

c x c y c x c yI u v A u v C u f v f C u f v f= + − − + + + (4)

where capital letters represent the results of Fourier Transform; and u and v represent frequencies in x and y directions in the frequency domain, respectively.

As the spatial frequencies of ( , )a x y and ( , )b x y are lower than 0,xf and

0,,

yf there are

three major peaks in the spectrum. The peak at the origin of the frequency domain is

a background signal ( , ),A u v while the other two peaks , ,

( , )c x c y

C u f v f− − and

*

, ,( , ),

c x c yC u f v f+ + which contain phase distributions, are distributed symmetrically on both

sides of the origin, as shown in Fig. 3.

383


Fig. 3. A spectrum of the fringe pattern after the Fast Fourier Transform.

Fig. 4. A continuous phase distribution obtained by the phase unwrapping process.

The spectra , ,

( , )c x c y

C u f v f− − or *

, ,( , )

c x c yC u f v f+ + can be intercepted correctly by using

a bandpass filter. This study filters out , ,

( , ),c x c y

C u f v f− − and shifts , ,

( , )c x c y

C u f v f− − to the

origin in order to eliminate the carrier frequency ,

cf where 2 2 1 2

, ,=( + ) .

c c x c yf f f The resulted

spectrum is then used in the Inverse Fast Fourier Transform to determine ( , ).c x y Then, the

phase distribution ( , )x yφ can be determined by:

Im[ ( , )]

( , ) arctan ,Re[ ( , )]

c x yx y

c x yφ

=

(5)

where: Re[ ( , )]c x y and Im[ ( , )]c x y are the actual and imaginary parts of ( , ),c x y respectively.

The result of (5) is between 2π− and 2.π According to the sign relation between the

numerator and denominator of (5), the phase distribution can be corrected to π− or ;π

however, the obtained wrapped phase still has a discontinuity. The phase unwrapping algorithm is introduced in this study to obtain a correct and continuous phase distribution [21], namely,

384


by checking whether the absolute value of the phase difference between each pixel and its

adjacent pixel is smaller than π; if the absolute value of the phase difference is larger than π, the phase value of the pixel must increase or decrease the integral multiple of 2π till the absolute value of the phase difference from the adjacent pixel is smaller than π. A continuous phase

distribution ( , )x yφ′ obtained by the phase unwrapping process is shown in Fig. 4. It is a pseudo

colour image mapping results of the entire image.

2.3. Measurement of surface profile and surface roughness

According to the definition of interference equation, the phase difference between a bright

fringe and a dark fringe is π, and the corresponding surface height difference is 4λ , where λ

is a wavelength of the light source. Therefore, a surface profile ( , )h x y corresponding to the

unwrapped phase is:

( , ) ( , ).4

h x y x yλ

φπ

′= (6)

The result is shown in Fig. 5a. Notice that the surface profile ( , )h x y in Fig. 5a contains a tilt

value.

a) b)

Fig. 5. A surface profile with a tilt value (a); an estimated tilt value (b).

In this study the least square method is used to fit the surface profile obtained by (6) into a plane, where the value of each point in this fitting plane can be approximated as a tilt value

corresponding to the surface profile. Let the equation of this fitting plane be:

( , ) ,h x y Dx Ey F∆ = + + (7)

where ( , )h x y∆ is a height of coordinates ( , )x y on the fitting plane, i.e. the tilt value; D, E and

F are parameters of the plane equation.

As the sum of distances from points in ( , )h x y to the plane represented by (7) is minimum,

the relationship of parameters D, E and F to ( , )h x y can be expressed in a matrix form as:

1

2

1 1 1 1

2

1 1 1 1

1 1 1

( , )

( , ) ,

( , )

n n n n

i i i i i i i

i i i i

n n n n

i i i i i i i

i i i i

n n n

i i i i

i i i

x x y x x h x y

D

E x y y y y h x y

F

x y n h x y

−

= = = =

= = = =

= = =

=

∑ ∑ ∑ ∑

∑ ∑ ∑ ∑

∑ ∑ ∑

(8)

385


where: n is the total number of pixels in the fringe pattern; ( , )i ix y are the coordinates of No. i

pixel in ( , )h x y ; and ( , )i i

h x y is a height of the pixel ( , )i ix y .

According to the parameters obtained by (8), the tilt value in Fig. 5a can be estimated, as

shown in Fig. 5b. The actual fibre end-face surface profile ( , )H x y can be calculated by:

( , ) ( , ) ( , ).H x y h x y h x y= − ∆ (9)

The surface roughness of the fibre end-face can be calculated based on the result of (9). In this study mean roughness (Ra) and root-mean-square roughness (Rq) are selected as the

measurement targets:

=

∑ |(

,) − ⟨,⟩|, (10)

=

∑ [(

,) − ⟨(,)⟩]/, (11)

where ( , )i i

H x y is an actual height of No. i pixel in the fringe pattern; and ( , )H x y is an

average of the actual height.

3. Experimental results and discussion

3.1. Experimental setup

This system obtains the fringe pattern of a fibre end-face on the principle of Fizeau

interferometer, and analyses the fringe pattern in order to measure the surface roughness. The O/E Part is placed on a mounting device, and an optical flat (λ/20 flat, Edmund Optics) is set up above the O/E Part. A red light semiconductor laser is used as the system light source

(λ = 632.8 nm). The laser light is expanded by the fibre bundle, the coaxial light is formed by a beam splitter, and two light beams with similar intensities are split. One light beam irradiates

the optical flat (reference surface) through a high magnification objective lens, while the other light beam irradiates the fibre end-face of the O/E Part; this beam is then reflected to the beam splitter to form the interference fringe with the reference light. Finally, a CCD camera captures

the fringe pattern. The proposed system framework is shown in Fig. 6.

Fig. 6. A structure of the proposed system.

386


The optical fibre on the O/E Part examined in this study consists of a fibre core, cladding,

and coating. The refractive index of the cladding is lower than that of the fibre core. The coating has a high toughness, which protects the optical fibre against damage. This optical fibre is a multimode fibre from Fibre Optic Communications, Inc. (FOCI), with a diameter of

125 μm; a diameter of the fibre core is 62.5μm, and the red or yellow plastic coating has a diameter of 600 μm (Fig.1).

3.2. Measurement results and analysis

The fringe pattern of the fibre end-face sample examined in this study is shown in Fig. 2a, and represents a region with an actual size of about 40 um × 40 um. The method proposed

in Section 2 is used for non-contact measurement of a surface profile and a surface roughness. First, the contrast of the interference fringe is enhanced, and the result is processed by the Fast Fourier Transform in order to obtain a corresponding spectrum. The required side-lobe signal

is intercepted by a filter, and processed by the Inverse Fourier Transform to obtain the phase value; a continuous phase distribution can be obtained by using the phase unwrapping

algorithm. Finally, the surface profile of the fibre end-face can be obtained by multiplying the unwrapped phase by a constant and deducting the tilt value. The result is shown in Fig. 7.

Fig. 7. A local surface profile of the fibre end-face obtained using the proposed method.

In order to validate the accuracy of the proposed method, the same fibre end-face sample

was measured by an AFM for comparison. AFM is a contact surface profile measurement

equipment, and its measurement accuracy is very high. However, the scanning speed is relatively low, therefore the contact probe may damage the surface structure of sample.

In addition, as the scanning area of AFM is limited, and the gap between the fibre core edge and the surface height of the O/E Part is large, the AFM probe is likely to break while scanning the fibre core edge; therefore it is inapplicable to inspection of the production line. In the

experiment, AFM measured only the local fibre end-face close to the fibre core centre to calculate its roughness. The area measured by AFM may be not completely consistent with the

area measured by the proposed method; however, the surface roughness of the sample in the same process varies only slightly. Therefore, the measurement result of AFM still can be an index in evaluating the accuracy of this method. The measurement result of AFM is shown in

Fig. 8. Rq corresponding to this local area is equal to 26.1 nm, and Ra − to 18.1 nm. Rq

calculated by the proposed method is equal to 23.4 nm, and Ra − to 19.2 nm. Comparison of the measurement results of this method with those of AFM shows that the Rq difference is equal

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to 2.7 nm, and the Ra difference − to 1.1 nm. Thus, the difference is within 3 nm. The scope of random variation in results and differences can be neglected as statistically insignificant.

Fig. 8. The measurement result of AFM of the local part of sample.

The measurement result of AFM can validate the accuracy of the method presented in this study. The structure of it is simple, and its cost is lower than AFM’s [21]. In addition, when a contact equipment is used to measure the body surface of unknown materials, SEM is

sometimes required to evaluate the measurement feasibility in advance. However, this study concerns a non-contact measurement; the surface profile of sample can be reconstructed, and

the surface roughness can be measured by only one fringe pattern with a spatial carrier, which is quite easily visualised and convenient. It should be considered in this system that, when a magnitude of the introduced spatial carrier is changed by adjusting the angle of the optical

flat if the introduced spatial carrier is too small, the side-lobe peak position and background signal peak position would be too close to each other after applying the Fast Fourier Transform.

As a result of this phenomenon, a partial background signal will be captured along with capturing the side-lobe, resulting in a measurement error. If the introduced spatial carrier is too large, the fringe contrast decays and cannot be correctly analysed.

4. Conclusions

As the flatness of a fibre end-face after laser cutting can significantly influence the coupling efficiency of the O/E Part and the fibre optic coupler, in this study there is proposed a surface

profile and roughness measurement system as a solution to analysing a fibre end-face. The hardware is based on the Fizeau interferometer in order to obtain the interference fringe

of a local fibre end-face on the O/E Part. Then, the phase data are calculated using the Fast Fourier Transform, and the local surface profile and surface roughness are reconstructed. In addition, the accuracy of the proposed algorithm is validated experimentally and with

a program. Compared with the measurement result of AFM, the corresponding roughness difference is less than 3 nm. This system can assist manufacturers to accurately screen too rough

optical fibre samples, and its measurement results can be a reference frame for improving the process.

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Acknowledgements

This research project was supported by the Ministry of Science and Technology, under Grant No. MOST 105-2221-E-035 -027.

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based on multi-value coding. Optik, 125(11), 2592−2596.

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with polarization phase-shifting Fizeau interferometer. Optics and Laser Technology, 39(2), 268−274.

[15] Tien, C.L., Yang, H.M., Liu, M.C. (2009). The measurement of surface roughness of optical thin films based

on fast Fourier transform. Thin Solid Films, 517(17), 5110−5115.

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contact method. Optik, 124(13), 1472−1476.

[17] Tien, C.L., Zeng, H.D. (2010). Measuring residual stress of anisotropic thin film by fast Fourier transform.

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Jun. 13, 2016; accepted on Jan. 22, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0029.


Index 330930, ISSN 0860-8229


DOPANT-BASED CHARGE SENSING UTILIZING P-I-N NANOJUNCTION

Roland Nowak, Ryszard Jabłoński Warsaw University of Technology, Faculty of Mechatronics, Św. A. Boboli 8, 02-525 Warsaw, Poland ([email protected], [email protected], +48 22 234 8633)

Abstract

We studied lateral silicon p-i-n junctions, doped with phosphorus and boron, regarding charge sensing feasibility.

In order to examine the detection capabilities and underlying mechanism, we used in a complementary way two

measurement techniques. First, we employed a semiconductor parameter analyzer to measure I−V characteristics

at a low temperature, for reverse and forward bias conditions. In both regimes, we systematically detected Random

Telegraph Signal. Secondly, using a Low Temperature Kelvin Probe Force Microscope, we measured surface

electronic potentials. Both p-i-n junction interfaces, p-i and i-n, were observed as regions of a dynamic behaviour,

with characteristic time-dependent electronic potential fluctuations. Those fluctuations are due to single charge

capture/emission events. We found analytically that the obtained data could be explained by a model of two-

dimensional p-n junction and phosphorus-boron interaction at the edge of depletion region. The results

of complementary measurements and analysis presented in this research, supported also by the previous reports,

provide fundamental insight into the charge sensing mechanism utilizing emergence of individual dopants.

Keywords: nanosensor, silicon, p-i-n junction, dopant, Kelvin probe force microscope.


1. Introduction

Rapid development of nanotechnology in the past 20 years also inevitably influences the field of metrology. The conventional sensors are not suitable anymore to be used in nano-

sized objects,due to their extremely small size and appearance of non-classical (i.e., quantum) effects. This is the main force driving the development of a new class of sensors – nanosensors.

Shortly, such sensors are able to detect and transduce information about objects (e.g. DNA molecules, nanoparticles, elementary charges) or phenomena (e.g. emission of photon, tunneling) in nanoscale. Nanosensors are constantly finding new potential applications

in medicine [1], biology, chemistry or physics [2]. Such sensors not only exhibit unique measuring capabilities, but are also expected to satisfy ever-growing demands regarding cost

effectiveness and considerably reduced power consumption. One of the main fields of interest is detection of single electrons or holes, mainly

in nanoelectronics or nanophotonics. Such sensors play an important role in nano-circuits,

where detection of changes of charge states is a critical and challenging task. Charge sensors are often constructed from various novel materials, including carbon nanotubes (CNTs) [3],

graphene [4] or molybdenum disulphide (MoS2) [5]. Such materials exhibit extraordinary properties, but fabrication processes are still challenging and the yield of successfully working devices remains relatively low.

In this work, we demonstrate a concept of charge (hole) [6] detection using a doped ultrathin silicon-on-insulator p-i-n junction. The p-i-n junctions, so far, are most commonly used

in applications involving light (photons) – photodiodes [7] or solar cells [8]. The study presented here attempts to elucidate also the possibility of charge detection.

R. Nowak, R. Jabłoński: DOPANT-BASED CHARGE SENSING UTILIZING …

The devices were fabricated in a clean room environment, by means of standard, widely-

used CMOS-compatible processes. Current-voltage (I−V) measurements, combined with the

results of surface electronic potential maps measured by a Low Temperature Kelvin Probe Force Microscope (LT-KFM), reveal importance of individual dopants in nanostructured silicon. In particular, mutual interaction between phosphorus (P) and boron (B) turns out to be

critical, thus classifying our device as a dopant-based sensor. As shown, such a P-B complex, when located at the boundary of depletion region, may determine operation of the entire device.

In addition, it is evidenced that, in fact, our devices are two-dimensional. Finally, we shortly address future steps concerning structure basic simulation and outline how to significantly raise a level of fabrication controllability.

The paper is organized in the following way: the device fabrication is described in Section 2,

in Section 3 we present and explain the results of I−V curves’ and surface electronic potential measurements, providing a detection mechanism concept based on P-B mutual interaction; Section 4 shortly addresses future works towards first-principle simulations and well-controlled fabrication processes. Finally, Section 5 concludes the paper.

2. Device fabrication process

The fabrication process of prototype devices is shown schematically in Fig. 1. In the first step, an original silicon-on-insulator (SOI) wafer was cut into 1 × 1 cm2 squares (Fig. 1a). After

that, the wafer squares were cleaned by means of ultrapure water, piranha solution (H2SO4 + H2O2, ratio 3:1) and with a help of an ultrasonic generator. Next, the top silicon layer was

thinned– the wafers were subjected to wet (with water vapor, 1000, 60 min × 2) and dry (900, 22 min) thermal oxidation and subsequent etching by a hydrofluoric (HF) acid. As a result, the top silicon layer was around20 nm thick, as confirmed by ellipsometer

measurements (Fig. 1b). In the next step, we proceeded with Electron Beam (EB) Lithography patterning, in order to create the desired shape of devices. Silicon etching was done by dry

Reactive Ion Etching (RIE). The anisotropic Si etching can use chemically reactive plasma (SF6

24 SCCM, O2 6 SCCM, RF Power 30 W, 15 s).

As shown in Fig. 1c, our devices consist of two relatively large SOI pads, connected by a constriction (channel). This specific shape arises from two reasons. First, our intention was to limit a parasitic capacitance that might affect LT-KFM measurements [9]. Such a capacitance

occurs between the cantilever pad and the underlying silicon layer. In our case, this silicon layer does not exist and the cantilever pad moves mainly over the SiO2 layer (buried oxide, BOX).

Secondly, as we attempted to examine the effects caused by discrete dopant atoms (donors or acceptors), it was convenient to have a limited number of them (in a statistical sense).

Fig. 1. 1 × 1 cm2 SOI wafers after cutting (a); the top silicon layer with a thickness of ~20 nm(b);

the top silicon layer with an EB-patterned structure of p-i-n junction (c); phosphorus doping (d);

boron doping(e); deposition of aluminum electrodes (f).

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After having formed the shape of our devices, we doped donors and acceptors, in both cases

by a standard thermal diffusion. First, we introduced phosphorus (P) donors into the n-type pad from spin-coated silica glass (OCD). During that, the p-type pad was covered by a thermally grown SiO2 10-nm-thick mask (Fig. 1d). Such a thickness assured that no donors diffused

through. Next, in a similar way, boron (B) acceptors were doped – Fig. 1e. This time, a poly boron film (PBF) was used as the boron source and the SiO2 mask became 15 nm thick. Our

design assumed that the p- and n-type pads were separated by a nominally 250-nm-wide i-type region. However, it must be mentioned that in reality, based on our experience, the alignment of masks during doping may be about 100 nm different than expected. Nevertheless, no overlap

of doping masks occurred. P (donors) and B (acceptors) concentrations are: ND ≈ 1 × 1018 cm−3

and NA ≈ 1.5 × 1018 cm−3, respectively, as estimated from secondary ion mass spectrometry (SIMS). The i-region (nominally undoped) is not purely intrinsic – SOI wafers have a native

low doping with B (NA ≈ 1 × 1015 cm−3). However, since the estimated number of B atoms in

the i-region is less than one per 10 nm3, it is reasonable to assume this region as intrinsic. Based on numerical simulations [31], it is expected that the lateral diffusion should not exceed several

tens of nanometres. Finally, in order to passivate the surface and protect it from contamination, a thin layer (2 nm) of SiO2 was grown on top (dry oxidation, 900ºC, 15 s). We know from our previous experience that it does not influence KFM measurements in a noticeable way [10].

In the last step the aluminum electrodes were created, Fig. 1f, by means of conventional

Physical Vapor Deposition (660ºC, 6 × 10−4 Pa). The aluminum pads, shown in Fig. 1f, have

a size of 600 × 600 µm2 and are 150 nm thick. Depending on the type of measurement (e.g.

floating or biased), we were able to apply a voltage. The fabrication process was described in detail elsewhere [32].


3.1. I−V characteristics in forward and reverse bias at low temperature

Figure 2a schematically shows the final device structure (the top Si thickness below 10 nm)

together with the measurement setup for I−V characteristics (a semiconductor parameter

analyzer, Agilent 4156C). The sample was inserted into a cryogenic high-vacuum (10−7 Torr) probe station (Lakeshore CPX-V). During measurements, the backgate was kept at VBG = 0 V

and, when needed, the voltage VSD was altered. Fig. 2b demonstrates typical I−V curves taken at a room temperature. As it can be seen, the devices exhibit a typical diode behaviour for forward and reverse biases.

Fig. 2. The measurement setup used for I-V curves’ measurements (a); a general I-V characteristic

for forward and reverse biases (b).

The appearance of effects caused by individual dopant atoms is expected mainly at low

temperatures, below 50 K. Fig. 3a and Fig. 3b show I−V curves taken again for forward and

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reverse bias conditions. As demonstrated, the nanoscale p-i-n junction also exhibits a typical

diode behaviour. However, the effect of parasitic resistance appeared and was reflected in the separation in the voltage domain – the threshold voltage of forward current shifted towards the positive direction (Fig. 3a), whereas the breakdown voltage shifted towards the negative

direction (Fig. 3b). This is caused by the insulating behaviour of silicon and dopant freeze-out effect [6, 23], both due to a low temperature. In order to overcome such a voltage drop in the

leads and to reach the junction area, a larger voltage must be applied. The dashed ovals in Fig. 3a and Fig. 3b indicate current fluctuations, which are not observed

at a room temperature. This current instability was confirmed by tracing the current as

a function of time. As a result, we detected step-like features, resembling current switching known as Random Telegraph Signal (RTS) [11]. In Fig. 3a, repeatability of RTS onset was

estimated to be at 9%, whereas in Fig. 3b − at 12%. RTS is well-known in submicron silicon

MOSFETs [12, 13] and also other similar devices. In those structures, however, RTS is primarily caused by deep-level traps located near an Si/SiO2 interface. This effect is not

considered in our study, as it will be explained in Section 3.2. Since the effects caused by individual dopants are more likely to emerge in smaller

structures, we also measured a narrower device, with its nominal constriction width

WC = 300 nm. As seen in Fig. 3c, the current measured for several values of VSD fluctuates mainly between two levels. Next, the raw RTS from Fig. 3c was digitized [14] and average time

intervals were plotted as a histogram – Fig. 3d. There are two prominent durations of time intervals. These time intervals correspond to a dopant charge state (ionized or neutral), as will be described in Section 3.3.

Fig. 3. I−V characteristics taken for the forward (a) and the reverse bias (b); the insets show RTS signals,

mainly with two levels; (c) two-level RTS vs. time measured for different VSD values;

(d) a histogram of low and high current levels.

3.2. Observation of surface electronic potential by Kelvin probe force microscope

In order to further study the observed RTS, we carried out surface electronic potential measurements by a Kelvin probe force microscope [15] (Unisoku Co., Ltd.). It proved to be a powerful tool for characterization of nanodevices, able to achieve even atomic resolution [16].

We used gold-coated silicon cantilevers (Seiko Instruments Inc.), which were scanning ~10 nm over the device surface (the constant height mode). The p-i-n nanojunction was measured

394


in ultra-high vacuum (UHV, 10−9 Torr). Since our read-out setup is based on piezoelectric crystals, the common problems with light-induced effects [17] do not appear here. The backgate

voltage was set to VBG = 0 V and no bias was applied to the n- or p-type pads, as shown in Fig. 4a (VREV = 0 V). The third voltage source, VKFM, is a part of KFM circuit. It is used to nullify the electrostatic force, which builds up between the point charge (e.g. an ionized dopant)

and the cantilever apex. The AFM image with a scan area for KFM mapping, marked by a dashed rectangle, is presented in Fig. 4b. Location of i-region (intrinsic) was estimated based

on the topography profile and marked by orange dashed lines. It is important to mention here that, due to the measurement conditions, the device was mounted upside-down, so in fact electronic potential mapping was done from the n- towards the p-type pad.

First, we measured the p-i-n junction at a low temperature T = 15 K. The result is presented in Fig. 4c. As we anticipated, based on the device structure, we observed 3 major flat electronic

potential sections, i.e. n-, i- and p-type regions. These regions are separated by localized-noise areas, which are marked in Fig. 4c by blue dashed ovals.

Based on the CMOS-compatible device fabrication process performed in a clean-room

environment, a density of interface states is expected to be in the order of 1010–1011 cm−2eV−1 or smaller [18, 19]. Thus, it can be estimated that in a 100 × 100 nm2 area around a given

interface (n-i or p-i), the number of interface traps (1–10) is negligible compared with the number of dopants (more than 200 dopants, P donors, and B acceptors). Based on that, dopant atoms (rather than interface states) are expected to give rise to any charging-related phenomena.

Hence, in analogy to the RTS described in the previous section, these temporal electronic potential fluctuations are also caused by the dynamic charging/discharging of dopant atoms that

are located within the n-i (and also i-p) interface.

Fig. 4. The KFM measurement setup (a); an AFM picture of the measured device with a scan area for KFM

measurements marked by a black rectangle (b); the surface electronic potential map with n-i

and i-p interfaces marked by blue dashed ovals (c); the n-i (d) and i-p depletion regions (e).

In the next step, we performed electronic potential mapping around depletion regions (n-i or p-i interfaces) marked in Fig. 4c. The results for n-i and i-p junctions are presented in Figs. 4d and 4e, respectively. As it can be clearly seen, time-dependent electronic potential fluctuations

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are again present. The next noticeable feature is that both interfaces have undulated shapes.

Those wavy edges could be ascribed to the local arrangement of dopants within a given interface [20]. Finally, if we compare widths of both interfaces (marked in Figs. 4a and 4b), we observe

that Wn−i ≈ 150 nm, whereas Wi−p ≈ 100 nm. The ratio of Wn−i/Wi−p corresponds to the ratio ND/NA (doping concentrations) and can only be observed in two-dimensional p-n (p-i-n)

junctions [21].

3.3. Sensing mechanism based on dopant atoms at depletion region boundary

of 2D p-n junction

As evidenced by the I−V curves (RTS) and KFM surface electronic potential maps (time-

dependent fluctuations), p-i-n junctions exhibit dynamic behaviour. To clarify the underlying

mechanism, a concept of active role of dopant atoms is introduced. For simplicity we consider an n-i interface (shown in Fig. 4d), where phosphorus donors are

interacting with boron acceptors. Taking into account the doping concentration (i.e. a higher concentration of phosphorus), it is likely that within the n-i interface region one boron acceptor

is surrounded by many phosphorus donors, as it is schematically shown in Fig. 5a. In fact, these donors, due to the superposition of electronic potentials, create a cluster [22]. In such a cluster,

an ionized boron (B− state) acceptor raises a local electronic potential, limiting the flowing current. This situation corresponds to the ionized state, defined in the left part of Fig. 5c as a lower current level in RTS. On the other hand, when a hole is captured by a boron, its state is changed to the neutral (B0 state). Consequently, the electronic potential within a cluster is

lowered and a larger current may flow – Fig. 5b. This case reflects a neutralized state, i.e. a higher current level in RTS, as depicted in the right part of Fig. 5c.

Fig. 5. A B acceptor in the ionized state (a); A B acceptor in the neutral state (b);

A schematic of RTS with assigned the abovementioned states (c).

Detection of time-dependent noise, either RTS in I−V curves or electronic potential fluctuations in KFM images, would not be possible without the presence of deep-energy level

dopants (primarily boron in this case). This is due to charge capture/emission time constants.

For conventional dopants, these times are far beyond the detection limits [23]. Existence of such deep-energy level dopants is expected in ultra-small structures, ideally – in structures with reduced dimensionality [24, 25]. Considering this, together with a thickness of top-Si, we

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concluded that the measured devices are truly two dimensional (2D). Another supporting fact

comes directly from the KFM images and is related to the width of depletion regions, as discussed in Section 3.2.

The two-dimensional character of our device brings further consequences regarding its basic

properties. It was theoretically predicted that the electric field within a depletion region, due to limited screening of host silicon, is very high [21] and penetrates outwards (confirmed

experimentally [18, 28]), which may increase efficiency of electron-hole separation and, thus, increase sensitivity. Next, the electric field is also almost independent of the applied bias; therefore the breakdown voltage is considerably higher than in conventional p-n junctions.

Moreover, the junction capacitance is very small, thus enabling to apply thedevice as a high-frequency diode, e.g. a photodetector. Finally, the width of depletion region is a linear function

of applied voltage, which makes the adjustment also linear [21]. It is important to mention that the proposed model is valid for a cluster located favorably

close to the edge of depletion region. Otherwise, charging/discharging boron atoms does not

alter the local electronic potential sufficiently and RTS becomes unobservable. In other studies, for the purpose of RTS characterization, a concept of “sensitive region” was introduced

[26, 27]. Such a region starts at the edge of depletion region (interface) and extends up to some length, usually several nanometres, towards the junction. Finally, the described model

of sensing mechanism can also be adapted to the opposite case – when a phosphorus atom is

embedded in a cluster of boron atoms.

4. Future steps

At a current level, location of dopants within a silicon lattice is random by nature and cannot be controlled. This is due to the fabrication processes, mainly the thermal diffusion used for

introduction of dopant atoms into the host silicon. Therefore, as the next step of research, it is desired to produce such devices with a highest possible accuracy regarding a precise location

of dopant atoms. In other words – by means of deterministic doping, e.g. using either ion implantation (SII) [29] or so called STM-Lithography [30].

Together with the experimental approach, theoretical studies are strongly desired.

In particular, the basic electrical properties should be simulated. In fact, we performed first steps in this direction. We obtained first results performing ab initio calculations (Atomistix

ToolKit) for a simple P-B-P complex inserted into a 2-nm-long Si nanowire (Fig. 6a) [31]. The results are presented in Fig. 6b. The Density of States (DOS) as a function of energy reveals that, despite a very short separation (0.5 nm), the ground states of P (a blue dashed line) and B

(a red dashed line) atoms are preserved. It means that, even in such an extremely small structure, dopants can be ionized and work as charge traps. This finding further supports our model

presented in the previous section. It is necessary, however, to carry out an ongoing study and simulation of larger structures with more dopants.

Fig. 6. The calculated structure containing a P atom surrounded by two B atoms (a);

DOS with marked the ground states of donor and acceptor (b).

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5. Conclusions

Summarizing, we have presented the results of basic studies devoted to modern p-i-n junctions. The examined devices, due to the used fabrication methods, offer a potentially high

integration level for integrated circuits’ applications. The charge detection mechanism is ascribed to the charging/discharging of a deep-level

boron atom. Such a charging/discharging phenomenon is manifested by current fluctuations

(RTS) in the I−V characteristics and time-dependent electronic potential fluctuations in the KFM images. The mutual interaction between donors and acceptors has been proposed as a model of charge sensing mechanism.

Our devices combine unique properties due to reduced dimensionality and individuality of dopants, which exhibit deeper-energy levels. We believe that this work will contribute to

a better understanding of new class of sensors – dopant-based nanosensors.

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Jun. 06, 2016; accepted on Jan. 29, 2017; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0033.


Index 330930, ISSN 0860-8229


COMPARISON OF INTERPOLATORS USED FOR TIME-INTERVAL

MEASUREMENT SYSTEMS BASED ON MULTIPLE-TAPPED DELAY LINE

Dariusz Chaberski, Robert Frankowski, Maciej Gurski, Marek Zieliński

Nicolaus Copernicus University, Faculty of Physics, Astronomy and Informatics, Grudziądzka 5, 87-100 Toruń, Poland ( [email protected], +48 56 611 2417, [email protected], [email protected], [email protected])

Abstract

The paper describes the construction, operation and test results of three most popular interpolators from

a viewpoint of time-interval (TI) measurement systems consisting of many tapped-delay lines (TDLs) and

registering pulses of a wide-range changeable intensity. The comparison criteria include the maximum intensity

of registered time stamps (TSs), the dependency of interpolator characteristic on the registered TSs’ intensity, the

need of using either two counters or a mutually-complementing pair counter-register for extending a measurement range, the need of calculating offsets between TDL inputs and the dependency of a resolution increase on the

number of used TDL segments. This work also contains conclusions about a range of applications, usefulness and

methods of employing each described TI interpolator. The presented experimental results bring new facts that can

be used by the designers who implement precise time delays in the field-programmable gate arrays (FPGA).

Keywords: time interval, multiple-tapped delay line, quantization-and-nonlinearity minimization, FPGA, time-to-

digital converter.


1. Introduction

The task of a TI interpolator is to increase resolution of TI measurements. It simply reduces to the measurement of a distance between one chosen type of edge (usually the rising edge) of a signal and the beginning of the standard-clock period that directly precedes this edge. A typical

TI interpolator consists of one or two TDLs and a register [1−4]. The way the register and TDL(s) are connected determines the way of TI interpolator operation and its use in the system.

Time-to-digital converters (TDCs) can have many applications and can be constructed

in many ways [1, 5−16]. TDCs can be used directly or indirectly to measure other quantities by converting them temporarily to TIs. Depending on a use domain and implementation technology TDCs can vary in properties and can differ in cost. The most important parameters

of TDCs are: a resolution of TI measurement, a measurement range and a maximum intensity of registered TSs [1, 4].

A measurement resolution of TDC can be improved by applying the Vernier method, interpolation and multiple-stage interpolation, time stretching or multiple measurement [1, 4]. The first three mentioned methods use TDLs and the TDC resolution is determined by the TDL

segment delay value. The TDL segment delay value can be decreased by changing the implementation technology to a finer one. The time stretching strongly decreases the maximum intensity of registered TSs but can be applied in conjunction with any other method. The multiple measurement can also be used jointly with any other method and can be performed

either in parallel or sequentially [17, 18]. When the multiple measurement is carried out in parallel there is no need to duplicate the whole meter. For TDL-based TDC only TDLs, code-converters and memory blocks have to be duplicated. In that case it can also be called

D. Chaberski, R. Frankowski, et al.: COMPARISON OF INTERPOLATORS USED FOR TIME-INTERVAL…

as multiple-TDL (MTDL)-based one. When the multiple measurement of TI is performed

sequentially, only a TI repetition block must be added to the measurement module. A measurement-range can be extended by implementation of a standard-clock period

counter, but it is limited by the long-term standard-clock stability. The maximum intensity

of registered TSs usually can be increased either by parallelization of critical TDC blocks or by changing the implementation technology to a faster one [19].

Currently the FPGA and Application Specific Integrated Circuit (ASIC) are two technologies that play an important role in implementation of TDC. Both these technologies enable to implement regularly placed elements of equal delay that are necessary to construct

TDLs [6, 7, 9−12, 19, 20].

When the multiple measurement is used, the correlation of measurement results plays an important role. If the measurement results are not correlated, the average value of standard

deviation of n measurements is decreased n times. If they are correlated, the correlation

degree and its nature should be considered. Highly correlated measurement results enable

to obtain more precise information about the real value − in comparison with those totally

uncorrelated measurements − when each measurement complements any other one [17, 18]. The way of using TDLs in this paper takes just advantage of this.

The results and conclusions contained in this paper can be useful for the designers who

implement and use time delays in FGPA structures. It mainly concerns TI generation systems as well as TI measurement ones. In the literature one can find information about the influence

of FPGA structure temperature deviations on the time delay of some FPGA primitives, such as look-up-tables (LUT). However, the influence of a clock frequency on the FPGA element delay value has not yet been published. We have noticed this effect during activation of a high-

resolution TI generator (an incremental resolution of 1 ps) based on TDLs constructed of LUTs, so we have decided to check whether a similar effect would appear in the case of TI

measurement systems. We suspect that this effect would play an important role in ring oscillators equipped with the enable input. When a ring oscillator has been enabled (started), the structure it has been implemented in is warming up, so a frequency of the generated clock

decreases till the temperature is stabilized.

2. Characterization of tested interpolators

There are many different ways of connecting TDL(s) and a register in order to obtain the possibility of TI interpolating. Fig. 1 shows the three ones tested by the authors. The first TI

interpolator (Fig. 1a) registers the state of TDL every rising edge of PULSES signal. The resolution of this interpolator depends on the TDL segment delay values [1, 19, 21]. It is very

convenient for this type of interpolator that the delay values of 1−n TDL segments

[ ]( , 0, 2 )ii nτ ∈ − directly create 1−n interpolator characteristic bins (quantization steps,

[ ]2,0, −∈ niqi

), but the 1−n -th TI interpolator quantization step is equal to the difference

between the standard-clock period T and the sum of just mentioned 1−n bin values, so:

∑−

=

−−=

2

0

1

n

i

inTq τ . (1)

In this case, when the TI characteristic changes, the number of quantization steps is constant. This fact simplifies the construction of further data processing blocks.

402


a)

b)

c)

Fig. 1. Three types of tested TI interpolators. PULSES signal registers the TDL state that represents the phase

of CLOCK (a); the TDL state that stores the history of PULSES signal is registered periodically

(every CLOCK cycle) (b); STOP signal chases START signal (c).

The second tested TI interpolator (Fig. 1b) stores the history of PULSES signal in the TDL. This history is periodically (every rising edge of CLOCK signal) written to the register and then

− if necessary (the chosen edge of PULSES signal appeared) − further written to memory. Please notice that in this case the register and memory write-ins are synchronized with the CLOCK signal rising edge. In the first type of tested TI interpolator the register and memory

write-ins are non-synchronous with CLOCK signal and synchronous with PULSES signal. This implicates that extension of a measuring range of this type of interpolator demands either a Grey

code counter (in this case the error is equal maximally to 1 and can be corrected later), two natural-binary counters or a mutually-complementing pair counter-register (in these both cases either the first or the second counter or either the counter or the register contains a proper state)

[22]. To extend a measuring range of the second type of TI interpolator (Fig. 1b) only one binary counter is sufficient. The third type of TI interpolator register and memory write-ins are

also (as it was in the case of the second type of tested interpolator) synchronized with CLOCK signal, so here also one binary counter suffices to extend the range of measurements.

For the second type of tested TI interpolator assigning a quantization step to the TDL delays

can be done in the same way as it has been done for the first type of interpolator. However, such an assignment for the third type of tested TI interpolator is usually done differently. Here, STOP

signal chases START signal. The shortest and the longest distances between START and STOP signals determine which flip-flops are active and which ones are not. So in this case the best

solution seems to be assigning the delay of the first active segment to the 0-th quantization step, assigning the delay of the second active segment to the 1-st quantization step, and so on. Please

notice that the segment delay is here equal to the difference ABττ − . The first and the last active

segments are usually used only partly, so statistically (the code-density test [2, 21, 23]) the

measured sizes of these segments are usually smaller than this difference. Three tested types of TI interpolators have different maximum intensities of interpolations.

The first one (Fig. 1a) has the highest maximum intensity of interpolations. Here, PULSES

signal can register the state of TDL independently of CLOCK signal. The maximal intensity of interpolation is limited only by the flip-flop propagation time. The maximum intensity

of interpolation of the second tested TI interpolator (Fig. 1b) is limited by the CLOCK signal

403


period. In this case, if two rising edges appear in the same CLOCK signal period, the first result

is overwritten by the second result. The third type of TI interpolator (Fig. 1c) has the lowest maximum intensity of interpolation, because it is limited by the total delay (the sum of all active segments delays) of the slower TDL.

It was found that, when the frequency of the clock that is passed through the TDL changes, the TDL segment delay value also changes. This is caused by the local semiconductor structure

temperature changes. This effect has been noticed for TI interpolators implemented in FPGA and it is supposed that a very similar effect appears also in ASIC. The TDL segment delay of the first type of TI interpolator is independent of the PULSES signal frequency because the TDL

is fed by CLOCK signal of a constant frequency. However, the characteristics of the second and the third TI interpolators depend on the PULSES signal frequency changes. This effect has

been examined thoroughly by the authors and the test results are described in the next sections of this paper.

When m TI interpolators are used, then the number of measurements increases m times.

A quantization step size of the measurement system that consists of m interpolators presented in Figs. 1a, 1b are inversely proportional to mn, where n is the number of TDL segments. However, when the measurement system consists of m TI interpolators presented in Fig. 1c, the

quantization step is proportional merely to mn – n +1. A deeper discussion about this feature is contained in Subsection 4.1.

To obtain a proper value of high-resolution quantisation step when m TI interpolators are

used, one has to calculate relative time offsets between TDL inputs when two first types of interpolators are used (Figs. 1a, 1b) [17]. When the third type of TI interpolator is used (Fig. 1c) these time offsets influence the selection of the first active segment in each TDL and

such calculations are needless [18].

Other types of TI interpolators can be found in [1−4, 20]. For example, in [20] the TDL delay elements have been created regarding the fact that the flip-flop propagation time tCQ is limited.

We have not tested this type of TI interpolator but we suspect that a similar influence of the intensity of registered pulses on the TDL characteristic would appear also for this solution.

3. Selected research topics

This section contains a description of some research issues that aim to complete the image of described research results. The following subsections describe the TI generator responsible

for providing a double PULSES signal and the methods used for examining the influence of the intensity of an event on the TI interpolator characteristic as well as the dependency of the maximum intensity of registered events on the TI interpolator type. The last subsection

describes some implementation details of tested TI interpolators.

3.1. TI generator

In order to compare TI interpolators the TI generator presented in Fig. 2 has been used.

The programmable frequency divider generates a rising edge every N CLK1 signal periods

(please refer also to Fig. 3). The programmable delay generates one CLK1 period-wide pulse

after M clock cycles since the CLKN1 signal rising edge appeared. Both pulse generators unify a width of the pulses (PULSE0 and PULSE1) and finally both these pulses are connected by the OR function. The signal created in this way is then just provided to the TI interpolator PULSES input.

404


Fig. 2. A block diagram of the TI generator used for testing TI interpolators.

Fig. 3. A timing diagram of the TI generator presented in Fig. 2.

The programmable generator is cycled by the CLK1 clock that is non-synchronous with the

standard-clock (CLK0) of TI interpolators. This feature enables to test every segment of TI interpolator. If these clocks were synchronous only a few selected segments would be tested.

The PULSES signal (Fig. 2) contains two TIs. The longer TI of a length ( )TMN − enables

to controllably test TI interpolator heating. The shortest TI of a length MT is measured by the

TI interpolator and the result (TI histogram) determines whether the tested interpolator works properly or not.

3.2. TI interpolator characteristic change observation method

It is generally known that the TDL characteristic depends on its temperature. For the

XILINX Virtex5 FPGA structure a temperature increase causes an increase of the TDL segment

delay. Fig. 4 shows an example of the dependence of TI interpolator characteristic on its

temperature. Please notice (the heating case) that, when the temperature increases, all (0−5, 7) but one (6) of TI interpolator quantization steps also increase. The 6-th quantization step decreases because its value is calculated accordingly to (1). Its value is not equal to the corresponding TDL segment value as it happens for the remaining quantization steps.

When all, except one, TI interpolator quantization steps have the same trend of changes and this one TI interpolator quantization step depends on the sum of remaining TI quantization

steps, then this one quantization step is the most sensitive to the temperature changes. The TI interpolator characteristic change observation method utilizes this fact. To obtain an average

TDL segment delay value q , the following formula is used:

1−

−

=

n

qTq m , (2)

where T is a standard-clock period; n is the number of quantization steps and qm is a quantization step given by (1).

In this paper not just the TDL segment delay dependence on ambient or average structure temperature has been examined, but also its dependence on the intensity of registered pulses.

When the intensity of these pulses increases, the temperature of TDL also increases and finally the TDL segment delay increases, too.

405


Fig. 4. Demonstration of the dependence TI interpolator characteristic on the structure temperature change.

3.3. Test of TI interpolator maximum intensity

The maximum intensity of the interpolator has been tested by checking whether this interpolator is able to operate properly and measure faultlessly at the maximum (theoretically

determined) intensity of pulses. If this test was passed, then it was checked whether this TI interpolator failed at a little bit higher frequency of pulses. If any of these two predictions had

appeared to be wrong, the TI interpolator model would have to be corrected.

3.4. Some implementation details

All tested TI interpolators have been implemented in the XILINX Virtex5 XC5VLX50

FPGA structure. The mentioned FPGA structure enabled to implement either 125 of 32 -

segment interpolators presented in Figs. 1a, 1b, or 50 of 80 -segment interpolators presented in

Fig. 1c. For all TI interpolators a standard-clock period of 10 ns was used. The period of this

clock fits the whole 32-segment TDL delay of the interpolator (Figs. 1a, 1b), so the average resolution is equal to about 312.5 ps for a single interpolator and to about 2.5 ps for all 125

interpolators. For the third TI interpolator (Fig. 1c) the number of quantization steps (the number of active TDL segments) was within a range from 66 to 69. From a practical point

of view the number of quantization steps has been reduced to 64 by software. In this case the average resolution of a single TDL was equal to about 156.25 ps and the resolution obtained for all 50 TDLs was equal to about 3.125 ps.

To create TDL segments LUT elements have been used. The effective delay of a segment of TDL constructed with the use of LUTs strongly depends on the route of the connecting wire.

This route depends mainly on the input of LUT that was used. To control a particular TDL

segment delay one has only to choose a proper LUT input − in most cases this operation is sufficient. This control is easily available when the design is made with the use of the FPGA

structure editor. When the design is described in Very High Speed Integrated Circuit Hardware Description Language (VHDL) a User Constraint File (UCF) can be used to limit the delay

of the path. Even when the design uses LUT1 (one input LUT component) the implementation process uses one but can use any input of the LUT. When a TDL is created as a macro (*.nmc file) then the situation is the same as when the TDL is described in VHDL.

4. Concept of multiple measurement

For every hit (Start, Stop or multi-Stop) a high-precision TS is obtained by finding the

common part of all TSs generated by this hit and registered by all TDLs. Fig. 5a explains these

operations when the total number of TDLs is equal to 4 . Each TS is represented by its beginning and its ending. The resultant high-resolution TS beginning is equal to the maximum

406


value of all TS beginnings, and − analogously − the ending of the high-resolution TS is equal

to the minimum value of all TS endings [17, 18, 24].

Please notice (Fig. 5a) that when the number (m ) of TDLs increases, the high resolution TS

is usually becoming narrower in this example (the resultant TS is better located). Finally, the

beginning of the high resolution TS for Start is determined by the beginning of 1,2 +i

E TS,

whereas its ending is determined by the ending of 1,3 −i

E TS. For the Stop hit the high resolution

TS is equally precise for 1=m or 2=m , but finally ( 4=m ) it becomes narrower and is

determined by the beginning of j

E,3

TS and the ending of 1,2 +j

E TS.

a)

b)

Fig. 5. The concept of multiple-measurement time-interval PDF calculation; an example of obtaining high-

precision time stamps from time stamps generated by four TDLs for two consecutive hits (a); time-interval PDFs

obtained for two consecutive time-stamp pairs depending on the number m of used TDLs (b).

It is very convenient to determine TIs as Probability Density Functions (PDFs). Then, while constructing a TI histogram not just only one point is added to it, but the PDF of this TI is added

and finally TI histograms are more accurate. These PDFs for TI can be calculated by the use of the Quantization and Non-linearity Minimization (QNM) method [24]. Fig. 5b explains obtaining PDFs for TS pairs (Start and Stop) in the case of multiple-measurement TDC. Here,

the PDF is a modified convolution (the sign of the first argument has been changed) of high-resolution TSs obtained for Start and Stop events. When TSs for Start and Stop are narrower,

then a TI can be determined more precisely and its PDF is higher and narrower (this is clearly visible in Fig. 5b).

Inaccuracy of calculation of the TDL offsets for TDCs based on both first interpolators (Figs. 1a, 1b) based on MTDL is the main source of TI calculation errors [17]. Every TS that depends on any quantization step of j-th TDL will be corrupted when j-th TDL offset is

inappropriately pointed out. Before calculating a high-resolution TS one has to calculate this offsets.

407


4.1. Increase of resolution

As mentioned in Section 2, an increase of resolution depends on the type of used TI

interpolators. When TI interpolators of the type presented in Figs. 1a, 1b are used, then the

resultant TI interpolator increases the measurement resolution mn times, but when the TI

interpolator presented in Fig. 1c is used − the measurement resolution increases 1+− nmn

times, where m is the number of TI interpolators and n is the number of segments in each TDL.

This difference is explained in Fig. 6.

Figure 6a shows the situation when each quantization step limit point of any TDL that is located within a reference TDL (TDL0) beginning and ending range creates a limit point in the

resultant TDL. In this case the TDL number 0 provides 1+n limit points and any other TDL

provides n limit points. The number of limit points is equal to 1+mn and the number

of quantization steps is equal to mn .

When each limit point of any TDL that is located within a range of minimum ( )StartStop tt −min

and maximum ( )StartStop tt −max difference between Stop and Start event appearance moments

creates a limit point in the resultant TDL (Fig. 6b), then ( )1−nm limit points are added to the

resultant TDL. For this TI interpolator type 2 additional points: ( )StartStop tt −min and

( )StartStop tt −max have to be added to the resultant TDL. In this way, ( ) 221 +−=+− mmnnm

limit points have been added that creates 1+− mmn quantization steps. a)

b)

Fig. 6. Explanation of the resolution increase mechanism for multiple TDL TDC; the resultant beginning

and ending are determined by the TDL0 beginning and ending (a); the resultant beginning and ending

are determined by the minimum and the maximum difference between Start and Stop pulses (b).

In this case no offset values between TDLs have to be calculated. Please notice (Fig. 6b) that

here these offset values are just coded as the first active segment index and its utilization. For

example, utilization of TDL2 first active segment (1,2

E ) is equal to 1,2

02,2

E

ee −

. When the delay

value of TDL2 increases by (a little) more than 1,20

ee − then 1,2

E will be utilised totally, and

0,2E will become the first active segment.

408


5. Experimental results

The experimental results mainly show the influence of registered pulses’ frequency on the

TI interpolator characteristic. Three types of interpolators (Figs. 1a, 1b, 1c) have been examined and the last type (Fig. 1c) of interpolator has been verified for two variants.

According to the expectations (Section 2), an average TDL segment delay does not depend on the pulses’ frequency for the first type of TI interpolator (Fig. 7, TDC0) and the TDL segment delay increases when the pulses’ frequency increases for the second type of TI

interpolator (Fig. 7, TDC1). The third type of tested interpolator consists of two TDLs. The first variant of this TI

interpolator is based on the fact that the bottom TDL (Fig. 1c) has been connected permanently to the standard clock (100 MHz), so its characteristic does not depend on the pulses’ frequency. However, the top TDL is connected to PULSES signal, so its characteristic depends on the

pulses’ frequency. For the second variant of this interpolator the bottom TDL is provided with the standard-clock cycle only when the pulse appeared, whereas the top TDL is connected to

PULSES signal exactly in the same way as in the first variant of this interpolator type. Here, the segment values of both TDLs increase when the frequency of pulses increases.

Fig. 7. The dependence of the (single/double) TDL segment average delay on the intensity

of registered PULSES.

Concluding, the average double TDL segment delay of the first variant of the third TI

interpolator type decreases when the pulses’ frequency increases (Fig. 7 TDC2), because the

difference ABττ − (Fig. 1c) decreases (

Bτ is constant and

Aτ increases) when the frequency

of pulses increases. The average double TDL segment delay of the second variant of this

interpolator increases, because both Bτ and

Aτ increase proportionally to their values and

ABττ > (Fig. 7 TDC3).

Figure 8 shows TI histograms between two pulses for every pair of pulses generated by the TI generator presented in Subsection 3.1. A nominal distance between pulses is equal to 10T,

where nsT 10= for all cases, so all histograms should be very similar, but they are not. One can

see that the TI histogram presented in Fig. 8a is Gaussian, but the rest of them are more or less disturbed at a location of 100 ns. The TI histograms presented in Fig. 8a are not disturbed, because this type TI interpolator characteristic (Fig. 1a) does not depend on the pulses’

frequency. For all TI interpolators the characteristics were measured when a frequency of pairs of pulses was equal to 1 kHz. However, the TI histograms presented in Figs. 8b, 8c, 8d are

disturbed because TDL(s) had different characteristic(s) during the TI measurements from those during the characteristics’ measurements. These disturbances result from the fact that a lot

of TSs have been registered into quantization steps that originally (1 kHz) were narrow (they

409


are now known as narrow ones) but after changing the frequency of pairs of pulses to 5 MHz

these quantization steps became wider because of a particular TDL quantization step beginning and ending shift (Fig. 6 may be helpful in imagining this process). Statistically, a wider TDL

quantization step counts more hits but the result is reported, accordingly to the original characteristic, with a higher weight (contributions to the TI histogram are higher and narrower).

The real characteristic is unknown, the characteristic that is used for calculation of the TI histogram is the best approximation that we know. The TDL characteristics are the only parameters of TDC that have changed; they changed accordingly to Fig. 7.

a) b)

c) d)

Fig. 8. The TI histograms between two pulses in a pair of pulses measured by the TI interpolator presented

in Fig. 1a, Fig. 1b, Fig. 1c, when the standard clock is permanently (c); conditionally connected to the bottom

TDL (d); when the intensity of pulse pairs is equal to 5 MHz and calculated when the characteristic of the TI

interpolator was measured when the frequency of pairs of pulses was equal to 1 kHz.

The authors also tested initially TDLs constructed of CARRY elements implemented

in XILINX Virtex4 XC4VLX25. A similar influence of the pulses’ frequency on the TDL segment delay has been noticed. However, for CARRY elements this influence was relatively

a little bit smaller and was equal to about %70 of that noticed for LUT elements in a tested

range from 500 Hz to 5 MHz of registered PULSES. The maximum intensity of registered PULSES of the TI interpolator presented in Fig. 1a

was equal to about 8104× pulses per second, 7

105× for the interpolator shown in Fig. 1b, and

only 61033× for both variants of the interpolator presented in Fig. 1c.

6. Conclusions

The experimental results and theoretical analyses have shown that the best type of interpolator for TI multi-measurement systems is that presented in Fig. 1a. The characteristic

of interpolator of this type does not depend on the registered pulses’ frequency, so when it is measured once (for one pulses’ frequency), it can be used for calculating TI between pulses

410


of other frequencies without causing errors. The measured TI histograms presented in Fig. 8

clearly confirm this statement. The authors performed in-depth tests of TDLs made of LUT elements and initial tests of TDLs made of CARRY elements. For both types of TDLs these characteristic changes are observed.

However, using this type of interpolator to extend a measurement range either two counters, a Grey code counter or a mutually-complementing counter-register pair are required, but this

hardware is needed only for one selected TI interpolator (the other interpolators just inherit this information). The only real difficulty of using TI interpolator of this type for multi-measurement systems is the need of calculating TDL offsets. Unfortunately, this operation

requires a lot of measurements and demands a lot of computational time. Also, for this type of TI interpolator the largest measuring intensity is allowed. The maximum intensities of other

interpolators are either limited by the standard-clock frequency or by the reverse of total TDL propagation time. Additionally, this one and the TI interpolators presented in Fig. 1b enable to obtain the highest ratio of resolution increase and the number of TDL segments.

The experimental results presented in this work show that for devices that use delay elements it is necessary to introduce an additional parameter that determines the frequency range within

which either control or measurement can be carried out with a guaranteed precision. To minimize the influence of pulses’ frequency change on the TDL characteristic change

one could use either a delay-locked or a phase-locked loop [20] for the TI interpolators

presented in Figs. 1b, 1c. This loop can be created by implementation of a dummy delay element that is placed nearby the stabilised TDL, so that this delay is sensitive to the temperature

of stabilised TDL and − what follows − is sensitive to the pulses’ intensity.

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[4] Szplet, R. (2014). Time-to-Digital Converters. In Carbone, P., Kiaei, S., Xu, F. Design, Modeling and Testing

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[5] Zieliński, M., Chaberski, D., Grzelak, S. (2003). Time-interval measuring modules with short deadtime.

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[15] Grzelak, S., Czoków, J., Kowalski, M., Zieliński, M. (2014). Ultrasonic flow measurement with high

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[16] Frankowski, R., Gurski, M., Płóciennik, P. (2016). Optical methods of the delay cells characteristics

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[19] Zieliński, M., Chaberski, D., Kowalski, M., Frankowski, R., Grzelak, S. (2004). High-resolution time-

interval measuring system implemented in single FPGA device. Measurement, 35(3), 311−317.

[20] Rahkonen, T., Kostamovaara, J. (1993). The Use of Stabilized CMOS Delay Lines for the Digitization

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[21] Frankowski, R., Chaberski, D., Kowalski, M. (2015). An optical method for the time-to-digital converters

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Aug. 15, 2016; accepted on Oct. 22, 2016; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0022.


Index 330930, ISSN 0860-8229


MODELLING OF MECHANICAL BEHAVIOUR OF HIGH-FREQUENCY

PIEZOELECTRIC ACTUATORS USING BOUC-WEN MODEL

Rafał Kędra, Magdalena Rucka

Gdańsk University of Technology, Faculty of Civil and Environmental Engineering, G. Narutowicza 11/12, 80-233 Gdańsk, Poland ([email protected], [email protected], +48 58 347 2497)

Abstract

The paper presents application of a modified, symmetrical Bouc-Wen model to simulate the mechanical behaviour of high-frequency piezoelectric actuators (PAs). In order to identify parameters of the model, a two-step algorithm

was developed. In its first stage, the mechanical parameters were identified by taking into account their bilinear

variability and using a square input voltage waveform. In the second step, the hysteresis parameters were

determined based on a periodic excitation. Additionally, in order to reduce the influence of measurement errors in

determination of selected derivatives the continuum wavelet transform (CWT) and translation-rotation

transformation (TRT) methods were applied. The results proved that the modified symmetrical Bouc-Wen modelis able to describe the mechanical behaviour of PAs across a wide frequency range.

Keywords: piezoelectric actuators, Bouc-Wen model, parameters identification.


1. Introduction

High-frequency piezoelectric actuators (PAs) are widely used as components of structural health monitoring (SHM) and damage detection systems based of the phenomenon of elastic waves’ propagation. They can operate in a wide frequency range, varying from 10 kHz to

500 kHz, depending on the properties of a monitored structure and the applied SHM method. The main advantages are their durability, small size and relatively low cost. High-frequency

PAs are available in a variety of shapes and configurations and they enable to excite both longitudinal and shear waves. Moreover, using multilayer piezo actuators enables to generate large amplitudes of excitation at a very low operating voltage. This last feature is especially

important because increasing the wave amplitude enables to extend the area monitored by an SHM system and to reduce the noise ratio. However, large amplitudes of excitations may

result in occurring nonlinearity between the applied voltage and the output displacement, caused by a non-linear relationship between the electric field and strain [1]. This is disadvantageous, since these nonlinearities significantly complicate the damage detection

process. Creation of a sensor model accurately describing its nonlinear mechanical behaviour at different voltage and frequency levels can be a solution of this problem. Numerous earlier

studies enabled to adapt many mathematical hysteresis models, including the ellipse model [2], the Preisach model [3], the Duhem model [4], the Backlash model [5], the Prandtl-Ishlinskii

model [6] and the Bouc-Wen model, to simulate the mechanical behaviour of PAs operating at low and medium frequencies. Especially the Bouc-Wen model has gained in popularity due to its ability to describe various non-linear and hysteretic systems. There are many modifications

of this model, which enable to consider the asymmetric hysteresis [7], the frequency-dependent behaviour [8] and the influence of pre-stressing [9]. Combining the rate-dependent Bouc-Wen

hysteresis model with a linear dynamic model enabled to model the shape of a displacement-voltage loop in a wide range of frequencies. The experimental tests exhibited a good agreement

R. Kędra, M. Rucka: MODELLING OF MECHANICAL BEHAVIOUR OF HIGH-FREQUENCY …

of the experimental and numerical results obtained for single [10] and multi-frequency

excitations [11]. The research have also indicated that a higher-order dynamic model is required to capture accurately the PA’s response for a wide range of excitation frequencies [12].

However, the previous studies have been carried out mainly for the voltage signal frequency not exceeding 1 kHz.

This paper presents the use of a modified symmetrical Bouc-Wen model for simulation of the mechanical behaviour of high-frequency piezoelectric actuators. A two-step algorithm dedicated to parameter identification is developed and experimentally verified on an example

of a multilayer piezoelectric plate actuator. The obtained results show that the Bouc-Wen model is able to describe the mechanical behaviour of piezoelectric actuators across a wide frequency

range.

2. Bouc-Wen model of hysteresis

The Bouc-Wen model has the ability to describe various non-linear and hysteretic systems.

It was formulated by Bouc [13] and extended by Wen [14]. Despite the fact that it does not have an exact analytical solution, the Bouc-Wen model has become a widely used one, due to its

comprehensiveness and mathematical tractability. In the case of PAs, besides their conventional formulation, a modified Bouc-Wen model is also used, wherein the hysteresis component is a function of the input voltage. That model can be expressed in a form of two differential

equations [15]:

hukxxkxcxm +=−++10000

)(ɺɺɺ , (1)

( [ sgn( ) ] ),n

h u A uh hβ γ= − +ɺ ɺ ɺ (2)

where: 0

m – the mass; 0c – the damping;

0k – the stiffness;

1k – the ratio of the input voltage

and the driving force; 0x – the initial displacement; x – a displacement; xɺ – the velocity; xɺɺ –

the acceleration; u – the input voltage; h – the restoring (hysteresis) component; and A, β, γ, n

– the hysteresis parameters. In a physical sense, the hysteresis component h may be treated as a non-linear component of the voltage-strain relation.

Fig. 1. Variability of the hysteresis component according to (2) for the following parameters:

β = 0.8, γ = –0.4, n = 1(a); A = 1, γ = –0.4, n = 1 (b); A = 1, β = 0.8, γ = –0.4 (c);

A = 1, β = 0.8, n = 1 (d); A = 1, β = 0.8, γ = –0.4, n = 1 (e); A = 0.5, γ = –0.04 (f).

414


Figures 1a–1d show the influence of individual parameters A, β, γ, n on a change

of hysteresis loops for the harmonic input voltage. An increase of the parameter A value causes a proportional increase in the value of hysteresis component h. The opposite effect has a change of the values of parameters β and γ. Moreover, an increase of those parameters reduces the slip

effect in the highest voltage area. An increase of the parameter n value leads to reduction of the hysteresis width and, to a smaller extent it is responsible for the smoothing effect. It can be seen

that, unlike other parameters, a change of the n value does not lead to a change of the hysteresis component variability in the initial period.

Figure 1e shows the result of a growth of the input voltage amplitude at constant hysteresis parameters. It does not affect the hysteresis amplitude but leads to an extension of the loop. The

effect of changing parameter values in the time domain is presented in Fig. 1f. Small values of β and γ result in a similarity of the hysteresis and the input voltage. The effect of the phase

shift may be obtained by disproportionate increasing one of them. It should be also noticed that (2) is frequency-independent for a mono-harmonic input voltage.

3. Methodology of parameter identification

Due to a strong nonlinearity of (1) and (2) describing the hysteresis behaviour of PAs, simultaneous identification of all its parameters is possible only by using iterative optimization

techniques such as the particle swarm optimization (PSO) [16], the genetic algorithm (GA) [17] and the differential evolution (DE) algorithm [18]. In PSO-based algorithms the initially

generated random groups of model and method parameters are called particles. The positions of particles are updated in subsequent steps, taking into account the defined velocity formula. By evaluating the model and calculating the fitness functions, the best location for each particle

and the entire group can be determined. Genetic algorithms are based on genetic operations. The response and the fit of a model are evaluated for all initial parameter sets. The best fitting

sets are selected to reproduction, crossover and mutation processes resulting in creation of new sets of model parameters. The selection and genetic operations are repeated until the stopping

criterion is achieved. DE is similar to GA, the differences lie in the way of carrying out genetic operations. Each new set of parameters is compared with a parent set and the set for which evaluation of the fitness value gives better results is passed to the next iteration. The main

problems of iterative approaches are their sensitivity to the initially selected parameters, the possibility of finding only a local minimum, and a relatively slow convergence. Therefore,

considering the equations (1) – (2) separately and determining parameters in subsequent steps without iteration is a very convenient alternative [8–9]. This approach significantly reduces the computational cost, simplifies the estimation procedure and enables to avoid ambiguity

in determining the parameters related to the occurrence of local minima of optimized functions. It may be used when the hysteresis amplitude is negligible in comparison with the amplitude

of the applied input voltage. Such a situation can occur in the case of excitation in a form of a periodic square function and, respectively, a low amplitude. This type of input signal can be defined by an infinite series of sine functions:

1

1

sin(2 (2 1) )4

2 1

Ssquare

k

k T tu B

k

π

π

−∞

=

−

=

−

∑ , (3)

where B denotes the amplitude and S

T − the period of the square function. In experimental studies the series (3) is limited to a finite number of initial terms. This feature of the excitation

signal significantly reduces the hysteresis component value. In the case of PAs operating in a range of frequencies below 1 Hz it is also possible to separate determination of parameters

associated with the static hysteresis [7].

415


3.1. Assessment of mechanical constants If only the first quarter of the square function period is considered, it can be approximated

by the Heaviside step function and used to determine the mechanical parameters using the limit

theorem. However, such a simplification does not take into account the time taken by a signal

to change from zero to its maximum value (the rise time) and − for the analysed high frequency

PAs, where the damping and mass values are much smaller than the stiffness one − it causes large errors. In order to reflect more accurately the variability of the input signal, it can be described as the difference of two time-shifted ramp functions with the same slope:

1 1 1

( ) ( ) ( )u at H t a t T H t T= ⋅ − − ⋅ − , (4)

where 1T is the rise time and a − the slope. Assuming that the influence of the hysteresis is

neglected ( uh << ) for the input voltage described by (4), the relation (1) after applying the Laplace transform can be written as:

2

0 0 0 1 1[ ( ) (0 ) (0 )] [ ( ) (0 )] ( ) ( )m s X s s x x c s X s x k X s k U s

− − −

− − + − + =ɺ , (5)

where: ( )( ) ( )X s x t= L ; ( )1 1( ) ( )U s u t= L and (0 )x

− , (0 )x−

ɺ are the initial displacement and

velocity of the PA, respectively. For the zero initial conditions, the relation (5) becomes:

1

1 1

12 2 2

0 0 0 0 0 0

(1 )( ) ( )

T sk k a e

X s U sm s c s k m s c s k s

−

−= =

+ + + +

. (6)

Using the theorem of the limit value, a series of steady-state parameters 0 1, , ,

nK K K… ,

can be specified. The first parameter is defined as:

0

1

1

0

2

0

3

0

1

0000

)1(lim)(lim)(lim)(lim

1

k

kTa

skscsm

eaksXstxtgK

sT

sstt

=

++

−

====

−

→→∞→∞→

, (7)

and the next ones are described by the following formula:

)(1

lim)(lim0

sgs

tgKi

si

ti

→→∞

== , (8)

where i

g is given by the recursive relationship:

∫ −−

−=

t

iiidgKtg

0

11)]([)( ττ . (9)

Calculation of the limits occurring in the previous formulas for i = 0, 1, 2, 3 enables to write

the following system of four nonlinear equations with four unknowns: 0

m , 0c ,

0k and

1k :

1

1 0

0

2 01

1 0 1

0 0

03 01

1 1 0 2

0 0 0

04 01

1 2 1 3

0 0 0

,

,2

,6

.24

kaT K

k

ckaT K K

k k

mckaT K K K

k k k

mckaT K K K

k k k

=

+ = + − = + − =

(10)

416


After multiplying all the equations by the stiffness factor k0, a linear system of equations

with zero values of all free terms will be obtained. This implies that the system (10) is indefinite and it enables to determine a solution only in the case when one of the unknown values is parameterized. In practice, it means that the model does not require determination of all

parameters but only their proportions. As a result, (10) can be written in a matrix form using only the first three equations:

=

−

−3

1

2

1

1

1

0

0

0

012

01

0

3

6

60

00

Ta

Ta

Tak

m

c

k

KKK

KK

K

. (11)

The mechanical parameters of the model are given by:

,1

k0

110

KTak = (12)

,2

k 0

1

2

0

1

110

−=

K

T

K

KTac (13)

.26

k2

0

11

3

0

20

2

1

0

2

1

110

−

−+=

K

KT

K

KKK

K

TTam (14)

The steady-state parameters 0

K , 1

K and 2

K can be determined experimentally using the

input voltage in a form of the square function with a sufficiently low amplitude and a long

period. The rise time 1T and the slope a can be determined based on the time variation of input

voltage. Finally, the equations (12) to (14) enable to determine the parameters 0

m , 0c and

0k

in relation to the parameter 1k . In order to avoid ambiguity, in the subsequent considerations

the arbitrary value of parameter 1k ,

1k = 1 V−1 was set.

3.2. Estimation of hysteretic parameters

Based on the known mechanical parameters, for any input voltage u it is possible to reproduce the corresponding hysteresis time variation h. The time derivatives of the hysteresis hɺ and input voltage uɺ can be also calculated using a simple differential scheme or other techniques of numerical differentiation. The parameters A, β, γ and n appearing in (2) can be

estimated using the averaging and the least squares methods. After denoting 1−= uhz ɺɺ and

hh = , deriving both sides of the (2) gives:

1

[ sgn( ) ] .n

z n u h h hβ γ−

=− +ɺɺɺ (15)

For time points, where 0>iihuɺ , the above equation can be rewritten in a discrete form:

1

( )n

i iiz n h hβ γ

−

= − +ɺɺ . (16)

After taking the logarithms of both sides and doing some mathematical manipulations, (16) can be rewritten as:

ln ln[ ( )] ( 1) lni

i

i

zn n h

hβ γ= − + + −

ɺ

ɺ. (17)

417


Linearization of (17) has been finally made by substituting )/ln(iii

hzq ɺɺ= , ii

hp ln= and

)](ln[ γβν +−= n . Thus, (17) can be written as a linear equation:

ν+−=iipnq )1( . (18)

The parameters n and ν can be determined using the least squares method:

( )

( )

( ) ( )∑∑

∑∑∑∑

∑∑

∑∑∑∑−

−

=

−

−

=2

1

2

2

2

1

2

2

lnln

lnlnlnlnln

ii

i

i

i

i

i

i

i

ii

iiiii

hNh

hh

zh

h

zh

pNp

pqpqp ɺ

ɺ

ɺ

ɺ

ν , (19)

( ) ( ) ( )∑∑

∑∑∑

∑∑

∑∑∑−

−

+=

−

−

+=2

1

2

1

2

1

2

1

lnln

lnlnlnln

11

ii

i

i

i

i

i

i

ii

iiii

hNh

h

zhN

h

zh

pNp

qpNqpn

ɺ

ɺ

ɺ

ɺ

, (20)

where 1

N denotes the number of considered time points. For the same set of time points, using the calculated value and a discrete form of (2), the parameter A can be computed according to

the formula:

∑ ∑−=

n

iih

n

e

Nz

NA

ν

11

11. (21)

In order to identify all hysteresis parameters, determination of ξ β γ= − is required. It can

be done by calculation of the average value of parameter ξ in 2

N time points for which the

relation 0<jj

huɺ occurs:

∑−

=n

jh

Az

N2

1ξ . (22)

Finally, the parameters β and γ can be calculated on the basis of ν and ξ:

n

e

22

νξβ −= , (23)

22

ξγ

ν

−−=

n

e

. (24)

The main disadvantage of the estimation procedure described above is the necessity of using

the second derivative, which significantly increases the effect of measurement errors. For this reason, in order to determine selected derivatives, the continuum wavelet transform (CWT) and the translation-rotation transformation (TRT) were used [19]. This method can significantly

reduce the impact of noise and it enables to eliminate the boundary effect of traditional wavelet differentiation. Firstly, the TRT of function f is defined by:

btatftf TRT−−= )()( , (25)

where:

max min

max min

( ) ( )f t f ta

t t

−

=

−

,

min min( )b f t a t= − . (26)

Afterwards, the derivative of function f can be calculated according to the formula:

1.5

( )TRT CWT

t

ff a

Ks ∆= +

ɺ, (27)

418


where ( )TRT CWTf is CWT of TRTf ,

t∆ is a time increment, s is the scale of CWT and K is

a parameter depending on the used wavelet function ψ and it is defined as:

∫∞

∞−

= dttK )(θ . (28)

A smoothing function θ is a time integral of the wavelet ψ with respect to time.

4. Determination of parameters of high-frequency piezoelectric actuators

In order to verify the described above method and its suitability for simulation of high-

frequency PAs, experimental examinations were made. The object of research was a Noliac

NAC2024 multilayer plate actuator (Fig. 2a) with dimensions 3 mm × 3 mm × 2 mm and an operating voltage in the range 0–200 V. A scheme of the experimental set-up is shown in

Fig. 2b. The input voltage signal was generated by a Tektronix AFG 3022 function generator and enhanced by an EC Electronics PPA 2000 high-voltage amplifier. The signal was then transmitted to the actuator causing its displacement, which was recorded by the scanning head

of Polytec PSV-3D-400-M laser vibrometer with a sampling frequency of 2.56 MHz.

Fig. 2. Laboratory tests: a scheme of the experimental set-up (a); high-frequency PAs (centimetre scale) (b).

Determination of the mechanical parameters was made using a rectangular excitation with

an amplitude of 7.8335 V and a period equal to 0.1 ms. Based on the measured input voltage

signal, two parameters (1T = 1.8672 μs and a = 4.1954 MVs-1) characterizing the excitation

were identified. In the second step, based on the PA displacements in a period of 0–45 μs,

a series of functions (0

g , 1

g , and 2

g ) and the steady-state parameters 0

K , 1

K and 2

K were

defined (Fig. 3). It can be seen that the values of functions 0

g and 1

g rapidly converge to their

limits, whereas for the function 2

g some oscillations are visible. It is related to the order

of magnitude of this function and can result in inaccuracies in the identified steady-state value

2.K The mechanical parameters determined based on the above-mentioned values are

summarized in Table 1.

Fig. 3. The functions used for identification of the mechanical parameters

of NAC2024 actuator: g0 (a); b) g1 (b); g2 (c).

419


The procedure described in Section 3.2 can be applied to any type of excitation. However, the numerical tests showed that the best results can be obtained for a sinusoidal input voltage

with a relatively large amplitude. The numerical tests also showed that in order to minimize the error associated with linearization, the identification procedure should be limited to a period in which the input voltage value is in a range of 25–75% of its amplitude. Therefore, to determine

the hysteresis parameters for the actuator, a harmonic excitation with a frequency of 10 kHz and a magnitude of 9.738 V was used. The time variability of hysteresis component was

determined on the basis of pre-determined mechanical parameters and the measured signal. In order to reduce the influence of noise, in determination of hɺ and hɺ the CWT-TRT method was applied (Figs. 4b–4c). In numerical calculations the first order Gaussian wavelet (Fig. 4a)

with a scale parameter 4s = and the parameter 42π=K

were used. It can be observed that using wavelet differentiation for h caused excessive smoothing in the jump area. However, this

interval was not considered in the identification process. All other derivatives, including the PA velocity and acceleration time variations were determined using the central differential scheme.

Fig. 4. Noise reduction for the hysteresis derivative: Gaussian wavelet of order 1 (a);

comparison of finite difference and CWT-TRT differentiation of hɺ (b);

comparison of finite difference and CWT-TRT differentiation of hɺ (c).

The three-stage process of determining the hysteresis parameters is visualised in Fig. 5.

In the first stage, the values of parameters ν and n were determined using the least squares method and fitting the linear regression model to experimental data (Fig. 5a). In next stages,

the values of A (Fig. 5b) and ξ (Fig. 5c) were determined by an averaging process. It can be noticed, that the experimentally determined data are scattered and no trend is clearly visible.

This is a result of using the second derivative and occurring noise which influence can be limited using the CWT-TRT method by increasing the scale parameter s. However, the performed numerical tests using the Gaussian noise have shown that it does not affect

correctness of the identification process. All identified parameters of (2) are listed in Table 1. Relatively low values of β and γ parameters indicate a small impact of non-linearity on the PA

behaviour.

Fig. 5. Visualization of determining the hysteresis parameters: identification of ν and n values using the least

square method (a); identification of A value (b); identification of ξ value (c).

420


Table 1. A list of identified parameters of NAC2024 actuator for the modified symmetrical

Bouc-Wen hysteresis model.

Parameter m0

[kg]

c0

[kgs−1]

k0

[Nm−1]

k1

[V−1]

A

[−]

β

[−]

γ

[−]

n

[−]

Identified

value

3.419 ×

10−4 491.632 3.725 × 108 1 0.192 0.034 −0.0463 1.419

5. Experimental validation and accuracy analysis

In order to assess suitability of the model, additional tests comparing the experimental data with the results of numerical calculations were carried out. The simulations were performed using MATLAB® ordinary differential equation solver ode45 on the basis of the identified

mechanical and hysteresis parameters and the experimentally measured input voltage signal. Selected results of the time variability of displacements and the hysteresis displacement-voltage

loop are given in Fig. 6. It can be seen that the numerical and experimental results are in a good agreement in both initial and steady-state periods. The qualitative assessment of the model accuracy was made on the basis of global goodness-of-fit measures: the error sum of squares

(SSE), the total sum of squares (SST), the R-squared (R2), as well as a local correctness coefficient – the maximum relative deviation (MRD):

2

1

ˆ( )N

i i

i

SSE x x

=

= −∑ , (29)

2

1

( )N

i

i

SST x x

=

= −∑ , (30)

21

SSER

SST= − , (31)

ˆmax| |

100%max

i i

i

x xMRD

x

−

= ⋅ , (32)

where: ix is the measured displacement;

ix is the numerically simulated displacement and x

is the mean value of ix . The calculated values of specified error measures at different

frequencies are summarized in Table 2.

Table 2. Statistical quantities characterizing the accuracy of predicted NAC2024 actuator displacements.

f [kHz] 10 20 40 60 80 100 120 140 160 180 200

SSE

[m]

2,22

× 10−15

2,52

× 10−14

5,78

× 10−15

2,27

× 10-15

2,14

× 10−15

2,46

× 10−15

3,19

× 10−15

3,28

× 10−15

3,34

× 10−15

5,2

× 10−15

4,39

× 10−15

SST

[m]

1,971

× 10−12

9,6

× 10−13

4,32

× 10−13

2,56

× 10−13

1,71

× 10−13

1,19

× 10−13

8,69

× 10−14

5,99

×10−14

4,33

× 10−14

3,26

× 10−14

1,94

× 10−14

x

[m]

−3,55×

10−11

−2,33×

10−11

−4,06×

10−11

1,08

× 10−10

−1,12×

10−10

−6,0

× 10−12

−2,25×

10−10

−3,41×

10−10

−1,12×

10−10

−1,44×

10−10

2,33

× 10−10

R2 [−] 0,999 0,974 0,987 0,991 0,987 0,979 0,963 0,945 0,923 0,840 0,774

MRD

[%] 5,776 17,317 12,080 10,538 12,333 16,065 17,073 23,027 34,450 49,211 63,879

The results of the error analysis indicate effectiveness of the Bouc-Wen model and the proposed parameter identification method of simulating high-frequency PA motion. For all

executed simulations in a range of 10–120 kHz, the correlation coefficient (R-square) between

421


the numerical and experimental results was greater than 0.95, which proves a good

correspondence of the theoretical model results with the actual physical PA behaviour. The best fit was obtained for a frequency of 10 kHz, which was used for the model calibration. Fig. 6 shows that the maximum absolute error occurs in the maximum applied voltage area.

An inaccuracy of the applied model significantly increases for frequencies of above 140 kHz. It is confirmed by a large value of MRD, at a level of 23% and more. An increase of the error

value is caused by a relatively high uncertainty in determination of the mass, which influences high frequency oscillations. In addition, the available sampling frequency in experimental studies does not provide a sufficient number of sampling points for a period in a range above

100 kHz.

Fig. 6. Comparison of the numerical and experimental results for NAC2024 actuator – displacement versus time

and displacement versus voltage in the initial stage, for a sinusoidal excitation with a frequency:

10 kHz (a); 60 kHz (b); 100 kHz (c); 140 kHz (d).

6. Conclusions

In the paper an improved two-step algorithm was proposed, dedicated to identifying the mechanical parameters of a modified, symmetrical Bouc-Wen model, adapted to characterize

high-frequency piezoelectric actuators. An increase of accuracy in the first step of identification process, compared with algorithms used for low frequency PAs, was obtained by taking into account the initial variability of the excitation signal and assuming the ability of its

approximation by a bilinear function. The hysteresis parameters of the Bouc-Wen model were determined in the second step, based on a single measured signal and using the CWT-TRT

method for reducing an influence of noise.

422


The proposed algorithm was applied to modelling the mechanical behaviour of a high

frequency PA. The Bouc-Wen model parameters were determined from the results of experimental tests using square and harmonic input voltage signals. Next, in order to validate the identification procedure, a comparative analysis was carried out. The tests aimed to compare

the experimentally measured displacements of the tested PA and the numerical results obtained for the identified parameters of the Bouc-Wen model. The performed analyses have shown

a good agreement between the experimental and numerical results in a range of 10–120 kHz. Above this range the model accuracy significantly decreases. It is caused primarily by inaccurate identification of the mass and by limitations of the assumed dynamic model.

The proposed method of identification can be used for different types of hysteretic systems. The obtained results can be also useful in numerical modelling piezoelectric transducers for

SHM systems.

References

[1] Sohrabi, M.A., Muliana, A. H. (2015). Nonlinear and time dependent behaviors of piezoelectric materials

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[2] Gu, G., Zhu, L. (2011). Modeling of rate-dependent hysteresis in piezoelectric actuators using a family

of ellipses. Sensors Actuat. A-Phys., 165(2), 303–309.

[3] Wang, X., Pommier-Budinger, V., Reysset, A., Gourinat Y. (2014). Simultaneous compensation of hysteresis

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[7] Zhu, W., Wang, D.H. (2012). Non-symmetrical Bouc-Wen model for piezoelectric ceramic actuators.

Sensors Actuat. A-Phys., 181, 51–60.

[8] Zhu, W., Rui, X.-T. (2016). Hysteresis modeling and displacement control of piezoelectric actuators with the

frequency-dependent behavior using a generalized Bouc-Wen model. Precis. Eng., 43, 299–307.

[9] Wang, D.H., Zhu, W. (2011). A phenomenological model for pre-stressed piezoelectric ceramic stack

actuators. Smart Mater. Struct., 20(3), 035018, (11 pp.).

[10] Wang, Z., Zhang, Z., Mao, J., Zhou, K. (2012). A Hammerstein-based model for rate-dependent hysteresis

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1391−1396.

[11] Wang, G., Chen, G., Bai, F. (2015). High-speed and precision control of a piezoelectric positioner with

hysteresis, resonance and disturbance compensation. Microsyst. Technol., (11 pp).

[12] Xu, Q. (2013). Identification and compensation of piezoelectric hysteresis without modeling hysteresis

inverse. IEEE T. Ind. Electron., 60(60), 3927−3937.

[13] Bouc, R. (1967). Forced vibration of mechanical systems with hysteresis. Proc. of the 4th Conference on

Nonlinear Oscillation., Prague, Czechoslovakia, 315.

[14] Wen, Y.K. (1976). Method for random vibration of hysteretic systems. J. Eng. Mech.-ASCE, 102(2), 249–

263.

[15] Low, T.S., Guo, W. (1995). Modeling of three-layer piezoelectric bimorph beam with hysteresis. IEEE J.

Microelectromech. Syst., 4(4), 230–237.

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[16] Wang, Z., Mao, J. (2010). On PSO based Bouc-Wen modeling for piezoelectric actuator. 3rd International

Conference on Intelligent Robotics and Applications., Shanghai, China, 125−134.

[17] Ha, J.L., Kung, Y.S., Fung, R.F., Hsien, S.C. (2006). A comparison of fitness functions for the identification

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_____________________________________________________________________________________________________________________________________________________________________________________

Article history: received on Feb. 17, 2016; accepted on Oct. 22, 2016; available online on Jun. 30, 2017; DOI: 10.1515/mms-2017-0019.


Index 330930, ISSN 0860-8229


EFFECT OF ADC RESOLUTION ON LOW-FREQUENCY ELECTRICAL

TIME-DOMAIN IMPEDANCE SPECTROSCOPY

Reyhaneh L. Namin, Shahin J. Ashtiani

University of Tehran, College of Engineering, P.O. Box 14395/515 Tehran, Iran ([email protected], [email protected], +98 21 8208 4952)

Abstract

In this paper, the effect of the resolution of an analogue-to-digital converter (ADC) on the accuracy of time-

domain low-frequency electrical impedance spectroscopy is examined. For the first time, we demonstrated that

different wideband stimuli signals used for impedance spectroscopy have different sensitivities to the resolution

of ADC used in impedance spectroscopy systems. We also proposed Ramp and Half-Gaussian signals as new

wideband stimulating signals for EIS. The effect of ADC resolution was studied for Sinc, Gaussian, Half-Gaussian,

and Ramp excitation signals using both simulation and experiments. We found that Ramp and Half-Gaussian

signals have the best performance, especially at low frequencies. Based on the results, a wideband electrical

impedance spectroscopy circuit was implemented with a high accuracy at frequencies bellow 10 Hz.

Keywords: electrical impedance spectroscopy, analogue-to-digital converter, Ramp signal, Fast Furrier transform,

Nyquist plot.


1. Introduction

Electrical impedance spectroscopy (EIS) is a non-destructive, inexpensive and simple

measurement method for testing properties of electrochemical or biological systems [1].This technique is widely used in several industrial and biological applications such as corrosion monitoring [2], study of the solar cells [3] fuel cells [4] and batteries [5], distinction between

normal and cancerous cells [6], and measurement of flowing blood to predict white thrombus formation [7].

The spectrum of impedance is a Nyquist plot, consisting of points that describe the magnitude and phase of the impedance for a specific frequency. The spectrum shape characterizes the order, structure, and the equivalent electrical model of a sample under test.

In EIS, the precision, frequency range, and test duration are very important. Since there is a possibility of change in the structure of the sample under test due to applying an excitation

signal for a long time, the duration of EIS has a high significance, particularly in studying biomaterials and medical applications.

The frequency range in which EIS is performed is determined by the sample. For instance, while in medicine the desired frequency range can be in the range of hundreds to a few thousand Hertz, it can be as low as a few mili-Hertz in battery and fuel cell applications [8, 9].

There are two general techniques used in EIS: the frequency domain and the time domain. In the frequency domain spectroscopy, a frequency is the independent variable and the

excitation signal is sinusoidal. To produce the impedance spectrum, the sinusoidal signal frequency is swept in the desired range [1].

While applying a sinusoidal excitation signal to the tested sample is one of the most

comprehensive and simplest methods for extraction of the impedance spectrum, it takes a long

R. L. Namin, S. J. Ashtiani: EFFECT OF ADC RESOLUTION ON LOW-FREQUENCY ELECTRICAL …

test time, especially at frequencies under 1 Hz [10]. Another issue of the method is its discrete

frequency components: for each desired test frequency, at least one period of sinusoidal signal in that frequency should be applied to the sample. Therefore, the number of frequency steps in the impedance spectrum is associated with the number of sinusoidal signals that are applied to

the sample under test. This results in lengthened test times, especially in low frequency ranges. In the time domain spectroscopy, time is the independent variable. To extract the impedance

as a function of frequency, a time-to-frequency transformation is needed. The transformation methods are generally based on Fourier [4], Laplace [11] or Wavelet [12] transforms. The excitation in the time domain spectroscopy is a wideband signal such as a multi-sinusoidal,

chirp, Sinc signal [10], a pulse or white noise [12]. An advantage of using a wideband signal is that by applying a single excitation, the impedance spectrum of the entire desired frequency

range can be obtained at once. This results in faster obtaining a more accurate spectrum, especially in low frequency ranges.

Since time-to-frequency transformations have to be done in the digital domain, an analogue-

to-digital converter (ADC) should be used. The resolution and sampling frequency of ADC has a significant effect on a precision of the impedance spectrum. If the ADC has an infinite

resolution and sampling frequency, the impedance spectrum has no error. However, in practice, using an ADC with a limited resolution and sampling frequency causes an error in the resulted impedance spectrum.

The ADC error associated with the limited resolution is generally modelled by the quantization noise. The general quantization noise theory predicts that the ADC error due to

a limited resolution is almost independent of the input signal and it just depends on the resolution [13]. However, our findings based on simulations and experimental results for the first time show that the shape of the excitation signals used in time domain EIS, has a significant

effect on the error of the measured impedance, when the ADC resolution is limited. In this paper, we examine the effect of ADC resolution on the error of the measured

impedance for several excitation signals, including Sinc, Gaussian, and half-Gaussian ones. In addition, we propose Ramp as a simple and accurate excitation signal for the time domain

EIS with a low sensitivity to ADC resolution. The purpose of this paper is − using a specific

hardware − to find an excitation signal which can result in an impedance spectrum with less errors.

In the next section, some excitation signals including the Ramp one, are introduced. In the

third section, the proposed method of implementing a wide-band impedance spectroscopy measurement system is presented. Finally, the results of the measurements are reported,

compared and analysed.

2. Excitation signals

To obtain an impedance spectrum, a small alternate current or voltage as the excitation signal

is applied to the sample and the response signal is monitored and measured. The ratio of the Fast Furrier Transform (FFT) of the response signal and the FFT of the excitation signal, as a transfer function, indicates the sample impedance.

Selection of an appropriate excitation signal − especially at low frequencies − is an important issue in EIS. A multi-sinusoidal excitation signal has been used in some previous research works [5]. This signal consists of 10 to 15 frequencies and the duration of applying the signal

is equal to the period of its lowest frequency. Using a multi-sinusoidal signal results in a shorter measurement time, in comparison with sinusoidal signals. A disadvantage of the multi-

sinusoidal signal is its discrete frequency components and elevated amplitudes. In some previous works a pulse signal is used as the excitation signal. It has a continuous

frequency spectrum. However, its high-frequency components drop off rapidly, resulting

426


in a lower accuracy at higher frequencies [14]. Moreover, for some specific frequencies,

the amplitudes of its components are equal to zero. A chirp excitation signal is also used in impedance spectroscopy systems. An advantage

of using this signal is its independent scalability in frequency and time. While it is an appropriate signal for EIS at higher frequencies, it is not very accurate at low frequencies

[12]. In this work, we used four excitation signals including Sinc, Gaussian, half-Gaussian and

Ramp ones for comparison. Fig. 1 shows the signals in the time and frequency domains. All

of these four signals have the same energy.

Fig. 1. Sinc, Gaussian, half-Gaussian and Ramp signals in the time and frequency domains.

Equations (1) to (4) define Sinc, Gaussian, Half-Gaussian and Ramp signals, respectively:

, (1)

, 0.98, (2)

0

, 2, (3)

∗ 15

0 " 15. (4)

Because of the presence of ADC and DAC the excitation signal is not ideal and the resolution and sampling frequency of ADC and DAC cause an error in the impedance spectrum. To extract

the impedance spectrum for frequencies below 1 Hz, the excitation signal should have a high amplitude in the time domain. Also, the excitation signal in the frequency domain should have a sufficient magnitude in a wide range of frequencies.

Figures 1a and 1b show a Sinc signal in the time and frequency domains, respectively. As can be seen, an amplitude of the Sinc signal in the time domain drops

427


rapidly. As a result, an ADC with a high resolution and sampling frequency is required. In the

frequency domain, the Sinc signal has an almost flat frequency spectrum but with a small value compared with other tree signals. In Figs. 1c and 1d a Gaussian signal in the time and frequency domains is shown. An amplitude of the Gaussian signal in the time domain is higher and is

changing slower than that of the Sinc signal. A magnitude of the Gaussian signal in the frequency domain is higher at lower frequencies and an increase of the frequency causes

a decrease of its magnitude, eventually dropping its value to zero. Figs. 1e and 1f show a half-Gaussian signal in the time and frequency domains. This signal is almost similar to the Gaussian one, but in the frequency domain its magnitude drops to zero in higher frequencies.

In Figs. 1g and 1h a Ramp signal in the time and frequency domains is shown. This signal has a higher amplitude in the time domain, and it also has a very high frequency-domain

magnitude at very low frequencies and its magnitude decreases by increasing the frequency. But, like the half-Gaussian signal, its magnitude drops to zero in frequencies higher than those for the Gaussian signal.

3. Effect of ADC quantization on impedance spectrum

As mentioned earlier, in the time domain EIS, the impedance signal should be converted to a digital one by an ADC. In this section, we briefly study the effect of the ADC resolution and an excitation signal on the accuracy of the impedance spectrum. To do this, an excitation signal with 3000 samples in 100 s, with a rate of 30 S/s, is applied to the first-order impedance, and then the response signal is quantized by a 14-bit ADC model in MATLAB. The difference

between the quantized signal at the ADC output and the input signal is calculated and then normalized to the amplitude of the least significant bit (LSB) of the ADC. Fig. 2 shows the

simulated quantization errors for Sinc, Gaussian, half-Gaussian and Ramp signals in the time domain. As can be seen, the quantization error of the Sinc signal has a larger value and exists in the entire duration of sampling. One explanation for the higher error of the Sinc signal is the

abrupt reduction in its time-domain amplitude. As a result, for a considerable part of the test duration, the signal amplitude goes well below the resolution of the ADC. While Gaussian,

half-Gaussian and Ramp signals have non-perfect frequency spectra compared with the Sinc signal, they have a smoother shape in the time-domain and for most of the test duration their

amplitudes are large enough to be detected by the ADC.

Fig. 2. The time-domain quantization error of Sinc, Gaussian, half-Gaussian and Ramp signals.

The errors are normalized to the amplitude of the least significant bit (LSB) of the ADC.

0 500 1000 1500 2000 2500 3000-1

-0.8

-0.6

-0.4

-0.2

0

Plot of Sinc signal

(a)

Error(L

SB

)

0 500 1000 1500 2000 2500 3000-1

-0.8

-0.6

-0.4

-0.2

0

Plot of Gaussian signal

(b)

Error (

LS

B)

0 500 1000 1500 2000 2500 3000-1

-0.8

-0.6

-0.4

-0.2

0

Plot of Half-Gaussian signal

(c)

Erro

r(L

SB

)

0 500 1000 1500 2000 2500 3000-1

-0.8

-0.6

-0.4

-0.2

0

Plot of Ramp signal

(d)

Erro

r(L

SB

)

428


For comparison, the root mean square (RMS) and mean quantization errors of the four

signals in LSB, are calculated and listed in Table 1.

Table 1. The RMS and mean quantization errors of Sinc, Gaussian, half-Gaussian and Ramp signals.

Signal Mean error (normalized to LSB) RMS error (Normalized to LSB)

Sinc −0.4608 0.3228

Gaussian −0.2428 0.1678

half-Gaussian −0.2147 0.1353

Ramp −0.2586 0.1664

As can be seen, the smallest quantization error is that of the half-Gaussian signal. The Ramp and Gaussian signals also have lower errors compared with the Sinc one.

To examine the effect of ADC on the impedance spectrum, Nyquist plots of the first-order impedance using the previous excitation signals are obtained by simulation using MATLAB. In the simulations, the ADC has a 14-bit resolution, its sampling frequency is 30 S/s, and

a duration of applying the excitation signal is 100 s. To obtain the electrical impedance spectrum in MATLAB, the excitation signal is quantized

and the FFT of the excitation signal is calculated, then this signal applied to the sample is again quantized and the FFT of the response is calculated. Eventually, by using some math operations,

the impedance spectrum is extracted. Figure 3 shows the sample circuit which has been used in the simulations. Table 2 contains

the values of components used in the simulations.

Fig. 3. The sample impedance circuit used for the measurements and simulations.

Table 2. The component values used in the simulations.

R1 R2 R3 C1 C2

0.5 KΩ 0.5 KΩ 0.5 KΩ 6.8 mF 10 uF

Figure 4 shows the simulation results. The ideal Nyquist plot is shown by the blue dots,

whereas the red dots represent the impedance spectrum obtained from the simulation.

According to the Nyquist plots resulted from Sinc, Gaussian, half-Gaussian and Ramp excitation signals, we perceive that the impedance spectrum errors for the Ramp and half-

Gaussian excitation signals are lower than the error which have been obtained by other excitation signals.

The effect of reduction of the ADC resolution on the impedance error is studied. Figs. 5 and 6 show average magnitude and phase errors of the impedance spectrum as a function of the

ADC resolution. As can be seen, for the Sinc signal, both phase and magnitude errors of the impedance considerably increase with decreasing the ADC resolution. The lowest sensitivity to the ADC resolution can be achieved by using Ramp or half-Gaussian signals.

429


Fig. 4. The Nyquist plots of the first-order sample obtained with Sinc (a); Gaussian (b);

half-Gaussian (c); Ramp excitation signals (d).

Fig. 5. The average magnitude error of simulated impedance spectrum as a function of the ADC resolution

for different excitation signals.

Fig. 6. The average phase error of simulated impedance spectrum as a function of the ADC resolution

for different excitation signals.

-500 0 500 1000 1500

-400

-200

0

200

400

Nyquist Diagram of Half-Gaussian excitation signal

Real Axis

(c)

-Im

ag

inary

Axis

-500 0 500 1000 1500-400

-200

0

200

400

Nyquist Diagram of Gaussian excitation signal

Real Axis

(b)

-Im

ag

ina

ry A

xis

-500 0 500 1000 1500

-400

-200

0

200

400

Nyquist Diagram of Sinc excitation signal

Real Axis

(a)

-Im

ag

ina

ry A

xis

-500 0 500 1000 1500-400

-200

0

200

400

Nyquist Diagram of Ramp excitation signal

Real Axis

(d)

-Im

ag

inary

Axis

8 9 10 11 12 13 14 15 160

0.5

1

1.5

2

2.5

Magnitude Error

ADC Resolution (Bit)

Ma

gn

itu

de

Err

or (

%)

Half-Gaussian

Ramp

Gaussian

Sinc

8 9 10 11 12 13 14 15 160

0.5

1

1.5

2

2.5

3

Phase Error


Ph

ase

Err

or

(deg

ree)

Half-Gaussian

Ramp

Gaussian

Sinc

430


4. Measurement and Test Setup

4.1. Design of Test Circuit

To test the effect of the ADC quantization error on the impedance spectrum for the four excitation signals, a test circuit has been designed. Impedance analyser designs use either

custom circuits [15] or application-specific integrated circuits (ICs), such as AD5833 [16]. In our case, since we need to study the effect of ADC resolution, we designed a simple specific

circuit with monolithic ADC and DAC ICs. Fig. 7 shows a block diagram of the test circuit. The circuit has analogue and digital sections. The analogue circuitry regulates the voltage applied to the sample and monitors the output current from the sample under test. It contains

op-amps U1-U5 and an instrumentation amplifier U6. The digital section executes signal processing and calculates the Fast Fourier transform.

Fig. 7. A block diagram of the electrical impedance spectroscopy system.

An excitation signal is generated by a microcontroller in the digital domain and is converted

to an analogue form by a digital-to-analogue converter (DAC). The amplitude signal is set by U2. Since a wide range of samples are non-linear, and because the Fast Fourier transform can be used only for linear systems, the amplitude of excitation signal should be small. In some

cases it is necessary to bias the sample with a specific DC voltage. U3 provides the DC voltage. U4 acts as a summing circuit and adds the DC and AC voltages. The excitation voltage is

applied to the sample by U5. The sample is placed between the inverting input of U5 and the ground. When the excitation voltage is applied to the sample, a current passes through the sample and then flows into the reference resistors. According to the impedance range of the

sample, one of the reference resistors is selected and the current passes through it. The voltage across the reference resistor has a linear relationship with the current passing through the

sample. This voltage is amplified by the instrument amplifier U6. The output of the instrument amplifier is connected to the analogue-to-digital converter, and afterwards the digital data are sent to the microcontroller for processing. The ADC resolution is 16 bits, but the effective

number of bits is 14 bits. Since the DAC output voltage is only positive, the DAC DC voltage source is used to adjust

the DC level of the excitation signal. In addition, in some EIS applications − such as

measurement of batteries and fuel or electrochemical cells − there is a need for a constant DC bias. In this case, the sample DC voltage along with the DAC DC voltage sources provide the required DC bias for the sample.

431


In the microcontroller, FFT of the response is calculated and used in the calculated FFT

of the excitation signal. In this case, the input signal is a voltage one and the output signal is a current one. Therefore, the transfer function represents the admittance of the sample under test. It is necessary to reverse the transfer function to obtain the impedance of the sample.

The DAC used in this system is AD5663 with a resolution of 16 bits. Op-amps U1-U4 are OP27 with a low offset voltage. AD620 is selected as the instrument amplifier due to its low

offset and noise level. The noise associated with the analogue electronic components, including the U1 to U6 and resistors at the ADC input, is simulated with SPICE. It is close to 850 nV rms which is much lower than the LSB of ADC. The selected ADC type is AD7988-5 that has

a sampling frequency of up to 500 kHz. The PIC33Fj128GP804 microcontroller type is used in this prototype for digital calculations. Fig. 8 illustrates the circuit board of complete test

circuit for impedance spectrum measurement.

Fig. 8. The circuit board of the electrical impedance spectroscopy system.

To transfer data from the microcontroller to PC and to plot the impedance spectrum, a USB interface is used. By deploying the serial interface, the real and imaginary parts of impedance

are separately sent to the computer and − with help of MATLAB − Nyquist plots of the measured impedance of samples are drawn.

4.2. Measurement results

To calculate the magnitude and phase errors of impedance spectrum, Sinc, Gaussian, half Gaussian and Ramp excitation signals are applied to the sample circuit shown in Fig. 3.

The values of components used in this measurement are the same as those in simulation, which is shown in Table 2. The impedance spectrum for various resolutions of the ADC is calculated. Figs. 9 and 10 show the RMS error in the measured impedance spectrum phase and magnitude

versus the ADC resolution. Figure 11 shows the impedance spectrum extracted by all the four excitation signals

presented in Fig. 1. As indicated in Fig. 11, the RMS error of the impedance spectra which are obtained from

the Ramp and half-Gaussian excitation signals are much smaller than the error obtained from

the Sinc excitation signal. As a result of reduction of the ADC resolution, the impedance spectrum error from the Sinc excitation signal has a faster increase rate. It should be noted that

the errors are obtained for the frequency range of 5 mHz to 10Hz. In all measurements, an ADC sampling frequency is set to 30 S/s. Also, the DAC generates data at a rate of 30 S/s.

432


Finally, in order to obtain the impedance spectrum in a wide range of frequencies and also

reducing the measurement points, three separate excitation signals were applied to the sample. The first excitation signal was applied to the sample for 100 seconds and its impedance spectrum in the frequency range of 5 mHz to 10 Hz is illustrated by the red circles in Fig. 12.

The second excitation signal was applied to the sample for 1 s, which presents the frequency range of 10 Hz to 100 Hz and is shown with the black squares. Finally, the last excitation signal

is also applied for 1 ms and its impedance spectrum frequency is up to 600 Hz and is displayed by the blue triangles. Fig. 12 shows the Nyquist plot obtained from these three excitation signals.

The reason of applying several excitation signals is that by using only one excitation signal for a wide range of frequencies, the FFT of signal is calculated with a fixed N; therefore for

higher frequencies the number of FFT points increases and thus the process takes a long time. The sample circuit used for this measurement is shown in Fig. 2, and the values

of components are shown in Table 3.

Fig. 9. The magnitude error of the measured impedance spectrum.

Fig. 10. The phase error of the measured impedance spectrum.

8 9 10 11 12 13 14 15 160

0.5

1

1.5

2

2.5

3

Magnitude Error


Mag

nit

ud

e E

rror

(%)

Half-Gaussian

Ramp

Gaussian

Sinc

8 9 10 11 12 13 14 15 160

0.5

1

1.5

2

2.5

3

3.5

4

Phase Error


Ph

ase

Erro

r (d

eg

ree)

Half-Gaussian

Ramp

Gaussian

Sinc

433


Fig. 11. The Nyquist plots extracted from measurement by using Sinc, Gaussian,

half-Gaussian and Ramp excitation signals.

Table 3. The values of components used for measurement of the impedance spectrum by using several

excitation signals.

R1 R2 R3 C1 C2

1 KΩ 1 KΩ 1 KΩ 6.8 mF 10 uF

Fig. 12. The Nyquist plot of the second-order sample obtained with 3 separate excitation signals.

5. Conclusion

In this paper, the effect of ADC resolution and the excitation signal shape in the time domain

impedance spectroscopy are for the first time studied simultaneously. We found that the excitation signal shape and the ADC resolution have a significant impact on the accuracy of the measured

-500 0 500 1000 1500-400

-200

0

200

400

Nyquist Diagram Half-Gaussian

Real Axis

(c)

-Im

ag

ina

ry A

xis

-500 0 500 1000 1500-400

-200

0

200

400

Nyquist Diagram Gaussian

Real Axis

(b)

-Im

ag

ina

ry A

xis

-500 0 500 1000 1500-400

-200

0

200

400

Nyquist Diagram SINC

Real Axis

(a)

-Im

ag

ina

ry A

xis

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-200

0

200

400

Nyquist Diagram Ramp

Real Axis

(d)-I

ma

gin

ary

Ax

is

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impedance spectrum. Several excitation signals are used in the time domain impedance

spectroscopy, such as Sinc and Gaussian ones. In this paper Ramp and half-Gaussian signals are also studied for the first time. These two new excitation signals are compared with the Sinc and Gaussian ones to figure out which of them generate a more accurate impedance spectrum when

the ADC resolution is limited. By applying all the four excitation signals for 100 s, the impedance spectra of each of them for a frequency range from 5 mHz to 5 Hz are extracted. Based on the

simulation and measurement results, the Ramp and half-Gaussian excitation signals result in lower RMS errors than those obtained from the Sinc and Gaussian signals. Also, with reduction of ADC resolution, an increase of the impedance spectrum error is higher than resulted from other signals.

Reference

[1] Lvovich, V.F. (2012). Impedance spectroscopy: applications to electrochemical and dielectric phenomena.

John Wiley & Sons.

[2] Hoja, J., et al. (2011). Method using square pulse excitation for high-impedance spectroscopy of

anticorrosion coatings. IEEE Trans. Instrum. Meas., 60(3), 957−964.

[3] Lohrasbi, M., et al. (2013). Degradation study of dye-sensitized solar cells by electrochemical impedance

and FTIR spectroscopy. Proc. of IEEE Energytech 2013, Cleveland OH, US, 1−4.

[4] Debenjak, A., et al. (2012). An assessment of water conditions in a PEM fuel cell stack using electrochemical

impedance spectroscopy. IEEE PHM 2012, Beijing, China, 23−25.

[5] Lindahl, P.A., et al. (2012). A time-domain least squares approach to electrochemical impedance

spectroscopy. IEEE Trans. Instrum. Meas., 61(12), 3303−3311.

[6] Kang, G., et al. (2012). Differentiation between normal and cancerous cells at the single cell level using 3-

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[7] Affanni, A., et al. (2012). Electrical impedance spectroscopy on flowing blood to predict white thrombus

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[8] Sanchez, B., Vandersteen, G., Rosell-Ferrer, J., Cinca, J., Bragos, R. (2011). In-cycle myocardium tissue

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[9] Rojo, L., Mandayo, G.G., Castafio, E. (2013). Thin film YSZ solid state electrolyte characterization

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[10] Kowalewski, M., Lentka, G. (2013). Fast high-impedance spectroscopy method using sinc signal excitation.

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[12] Nahvi, M. Hoyle, B.S. (2009). Electrical impedance spectroscopy sensing for industrial processes. IEEE

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[13] Widrow, B., Kollar, I. (2008). Quantization noise. Cambridge University Press.

[14] Ensheng, D., et al. (2010). A pulsed approach for electrical impedance spectroscopy measurement. ISDEA

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[15] Hoja, J., Lentka, G. (2013). A family of new generation miniaturized impedance analyzers for technical

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